How to learn to Love the BOSS Baryon Oscillations Spectroscopic Survey

Shirley Ho Anthony Pullen, Shadab Alam, Mariana Vargas, Yen-Chi Chen + Sloan Digital Sky Survey III-BOSS collaboration Carnegie Mellon University SpaceTime Odyssey 2015 Stockholm, 2015 What is BOSS ?

Shirley Ho, Sapetime Odyssey, Stockholm 2015 What is BOSS ?

Shirley Ho, Sapetime Odyssey, Stockholm 2015 BOSS may be …

Shirley Ho, Sapetime Odyssey, Stockholm 2015 SDSS III - BOSS Sloan Digital Sky Survey III - Baryon Oscillations Spectroscopic Survey

What is it ? What does it do ? What is SDSS III - BOSS ?

• A 2.5m telescope in New Mexico • Collected • 1 million spectra of , • 400,000 spectra of supermassive blackholes (), • 400,000 spectra of stars • images of 20 millions of stars, galaxies and quasars.

Shirley Ho, Sapetime Odyssey, Stockholm 2015 What is SDSS III - BOSS ?

• A 2.5m telescope in New Mexico • Collected • 1 million spectra of galaxies , • 400,000 spectra of supermassive blackholes (quasars), • 400,000 spectra of stars • images of 20 millions of stars, galaxies and quasars.

Shirley Ho, Sapetime Odyssey, Stockholm 2015 SDSS III - BOSS Sloan Digital Sky Survey III - Baryon Oscillations Spectroscopic Survey

What is it ? What does it do ? SDSS III - BOSS Sloan Digital Sky Survey III - Baryon Oscillations Spectroscopic Survey

BAO: Baryon Acoustic Oscillations AND Many others! What can we do with BOSS?

• Probing Modified gravity with Growth of Structures • Probing initial conditions, neutrino masses using full shape of the correlation function • Probing velocities of clusters via kinetic Sunyaev Zeldovich • Understanding the Intergalactic medium and dust in galaxies • /cluster evolution at lower redshift, quasars properties at high redshift • New way to Test Gravity using CMB lensing and BOSS

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Outline today

• What is really BOSS-BAO ? –What do we learn from it ? • What other science we can do with BOSS ? –Many… –Introduce a new probe combining BOSS AND CMB- lensing to learn about gravity at the largest scale !

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Outline today

• What is really BOSS-BAO ? –What do we learn from it ? • What other science we can do with BOSS ? –Many… –Introduce a new probe combining BOSS AND CMB- lensing to learn about gravity at the largest scale !

Shirley Ho, Sapetime Odyssey, Stockholm 2015 What are Baryon Acoustic Oscillations?

To measure BAO, we usually calculate the correlation function

Shirley Ho, Sapetime Odyssey, Stockholm 2015 What are Baryon Acoustic Oscillations?

What is the correlation function of population during the day?

20 miles 20 miles HOME/nearby school

Office

Office

Shirley Ho, Sapetime Odyssey, Stockholm 2015 What are Baryon Acoustic Oscillations?

What is the correlation function of population during the day?

A bump in 20 miles!

Shirley Ho, Sapetime Odyssey, Stockholm 2015 What are Baryon Acoustic Oscillations?

To measure BAO, we first calculate the correlation function

Shirley Ho, Sapetime Odyssey, Stockholm 2015 A bump at ~150Mpc BAO and Galaxies

• Pairs of galaxies are slightly more likely to be separated by 150 Mpc than 120 Mpc or 170 Mpc.

500 Mlyr

150 Mpc

Credit: Zosia Rostomian, LBNL

Shirley Ho, Sapetime Odyssey, Stockholm 2015 NOTE: BAO effects highly exaggerated here BAO as a Standard Ruler

• This distance of 150 Mpc is very accurately computed from the anisotropies of the CMB. Planck 2015 –0.4% calibration with current CMB.

Image Credit: E.M. Huff, the SDSS-III team, and the South Pole Telescope team. Graphic by Zosia Rostomian

Shirley Ho, Sapetime Odyssey, Stockholm 2015 SDSS III - BOSS

• In SDSS-III, we use maps of the large-scale structure of the Universe to detect the imprint of the sound waves. • We use 3 different tracers of the cosmic density map: – Galaxies at redshifts 0.2 to 0.7. – Quasars at redshifts 2.1 to 3.5. – The intergalactic medium as revealed by the Lyman α Forest, at redshifts 2.1 to 3.5. • We look for an excess clustering of overdensity regions separated by 150 Mpc

Shirley Ho, Sapetime Odyssey, Stockholm 2015 SDSS III - BOSS

• In SDSS-III, we use maps of the large-scale structure of the Universe to detect the imprint of the sound waves. • We use 3 different tracers of the cosmic density map: – Galaxies at redshifts 0.2 to 0.7. – Quasars at redshifts 2.1 to 3.5. – The intergalactic medium as revealed by the Lyman α Forest, at redshifts 2.1 to 3.5. • We look for an excess clustering of overdensity regions separated by 150 Mpc

Shirley Ho, Sapetime Odyssey, Stockholm 2015 SDSS III - BOSS

• In SDSS-III, we use maps of the large-scale structure of the Universe to detect the imprint of the sound waves. • We use 3 different tracers of the cosmic density map: – Galaxies at redshifts 0.2 to 0.7. – Quasars at redshifts 2.1 to 3.5. – The intergalactic medium as revealed by the Lyman α Forest, at redshifts 2.1 to 3.5. • We look for an excess clustering of overdensity regions separated by 150 Mpc

Shirley Ho, Sapetime Odyssey, Stockholm 2015 A Slice of BOSS

Credit: D. Eisenstein

Shirley Ho, Sapetime Odyssey, Stockholm 2015 BAO in BOSS Galaxies

• Clustering Analysis of the BOSS galaxy sample has produced the world’s best detection of the late- time acoustic peak.

Anderson et al. 2014; s (Mpc/h) Vargas, Ho et al. 2014; Tojeiro et al. 2014

Shirley Ho, Sapetime Odyssey, Stockholm 2015 BAO in BOSS Galaxies

• Clustering Analysis of the BOSS galaxy sample Before Reconstruction has produced the world’s best detection of the late- time acoustic peak. s Galaxy Correlations Galaxy

Anderson et al. 2014; s (Mpc/h) Vargas, Ho et al. 2014; Tojeiro et al. 2014

Shirley Ho, Sapetime Odyssey, Stockholm 2015 BAO in BOSS Galaxies

• Clustering Analysis of the BOSS galaxy sample After Reconstruction has produced the world’s best detection of the late- time acoustic peak.

150 Mpc Galaxy Correlations Galaxy

Anderson et al. 2014; Vargas, Ho et al. 2014; Tojeiro et al. 2014

Shirley Ho, Sapetime Odyssey, Stockholm 2015 BAO in BOSS Galaxies

• The peak location is measured to 1.0% in our z = 0.57 sample and 2.1% in our z = 0.32 sample

150 Mpc Galaxy Correlations Galaxy

Anderson et al. 2014; Vargas, Ho et al. 2014; Tojeiro et al. 2014

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Outline today

• What is really BOSS-BAO ? –What do we learn from it ? • What other science we can do with BOSS ? –Many… –Introduce a new probe combining BOSS AND CMB- lensing to learn about gravity at the largest scale !

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Constraining cosmological models

Planck 2015

Shirley Ho, Sapetime Odyssey, Stockholm 2015 How about ?

• Combined constraints on Dark Energy

BOSS collaboration 2014

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Is it a cosmological constant?

• Combined constraints:

cosmological constant?

BOSS collaboration 2014

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Or is it Dark Energy?

• Combined constraints:

Dark Energy instead of a steady cosmological constant?

BOSS collaboration 2014

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Comparison with other probes

BOSS collaboration 2014 Black: Planck +BAO + SN

Lensing, clusters Redshift Space Lya 1D P(k) Distortions Shirley Ho, Sapetime Odyssey, Stockholm 2015 Outline today

• What is really BOSS-BAO ? –What do we learn from it ? • What other science we can do with BOSS ? –Many… –Introduce a new probe combining BOSS AND CMB- lensing to learn about gravity at the largest scale !

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and Large Scale structure

ds2 =(1+ )dt2 a2(1 + 2)dx2

Zhang, Liguori, Bean, Dodelson 2007

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and Large Scale structure: Introducing EG

ds2 =(1+ )dt2 a2(1 + 2)dx2

Zhang, Liguori, Bean, Dodelson 2007

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and Large Scale structure: Consider GR

ds2 =(1+ )dt2 a2(1 + 2)dx2

GR

Zhang, Liguori, Bean, Dodelson 2007

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and Large Scale structure: Modifying Gravity!

ds2 =(1+ )dt2 a2(1 + 2)dx2

GR

modified gravity

Zhang, Liguori, Bean, Dodelson 2007

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and Large Scale structure: General equation of EG

ds2 =(1+ )dt2 a2(1 + 2)dx2

GR

modified gravity

Zhang, Liguori, Bean, Dodelson 2007

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and LSS Space (frequency) and time (redshift) dependence of EG

Pullen, Alam & Ho, 2015

µ =1 =1 if it is General Relativity

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and LSS Space (frequency) and time (redshift) dependence of EG

Pullen, Alam & Ho, 2015

if it is f(R) gravity

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Testing Gravity by combining CMB lensing and LSS Space (frequency) and time (redshift) dependence of EG

Pullen, Alam & Ho, 2015

if it is chameleon model

Shirley Ho, Sapetime Odyssey, Stockholm 2015 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 We nowg translategg these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus, E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 We begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- r r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightings within each redshift sample. Also, in order gular quantities, we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and C` as 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g estimate given in the public Planck CMB lensing map. where2 z ¯ is the average redshift of theg galaxy2 sample. C` 2 linear atgg smaller2 scales than for density perturbations. is the [ galaxy-convergenceEG(`, z¯)] angular(C` cross-power) spectrum,() We expect(C` ) these e↵ectsThe to be totalsmall and number will neglect of them galaxies (or quasars) within each givenWhy on small does2 scales it= usingmatter the Limber thatg approximation we+ use CMB by + lensingin ourgg forecasts. instead(17). ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` 4. FORECASTS C` = d W ()fg()g P 2( )g ,z (13), 2 r In this section we willfrom predict Samushia the ability et of al. current (2014) to set b[CMASS]=2.16 and The- Dramatically uncertaintyZ1 increase in C` can the be z-range written✓ ◆ asof the tracers you can use and future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where- wefg isknow the galaxy the( redshiftC z gof)2 distributionCMB+(C lensing+ andNW (exactly)()=Cgg +tween N(nogg GR)photo-z and MG models.needed)sample In all have⇠ our not forecasts been we measured will model-independently for (1 /2CMB)g is the CMB` lensing kernel.` In order` to` assume GR when calculating uncertainties. We describe match- no the intrinsic( kernelC` )= in the alignment galaxy-convergence of CMB power spec- , (18) DR11, so we assume a 10% measurement of and, as in (2` + 1)fsky the sensitivity of the measured EG with the signal-to- trum, we define C✓g, the velocity-galaxy angular cross- Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use - But we are` working on teasing out anynoise systematics ratio (SNR) of now.EG marginalized over angular scale power spectrum, to be and redshift, given by where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 We nowg translategg these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus, E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 We begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- r r 2c Cˆ tracer-CMB lensing (b)publicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightings within each redshift sample. Also, in order gular quantities, we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to RedshiftEGgg(`, z¯)= space distortions, (1/b)(12) tracer-tracer clustering (b*b) 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and C` as 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g estimate given in the public Planck CMB lensing map. where2 z ¯ is the average redshift of theg galaxy2 sample. C` 2 linear atgg smaller2 scales than for density perturbations. is the [ galaxy-convergenceEG(`, z¯)] angular(C` cross-power) spectrum,() We expect(C` ) these e↵ectsThe to be totalsmall and number will neglect of them galaxies (or quasars) within each givenWhy on small does2 scales it= usingmatter the Limber thatg approximation we+ use CMB by + lensingin ourgg forecasts. instead(17). ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` 4. FORECASTS C` = d W ()fg()g P 2( )g ,z (13), 2 r In this section we willfrom predict Samushia the ability et of al. current (2014) to set b[CMASS]=2.16 and The- Dramatically uncertaintyZ1 increase in C` can the be z-range written✓ ◆ asof the tracers you can use and future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where- wefg isknow the galaxy the( redshiftC z gof)2 distributionCMB+(C lensing+ andNW (exactly)()=Cgg +tween N(nogg GR)photo-z and MG models.needed)sample In all have⇠ our not forecasts been we measured will model-independently for (1 /2CMB)g is the CMB` lensing kernel.` In order` to` assume GR when calculating uncertainties. We describe match- no the intrinsic( kernelC` )= in the alignment galaxy-convergence of CMB power spec- , (18) DR11, so we assume a 10% measurement of and, as in (2` + 1)fsky the sensitivity of the measured EG with the signal-to- trum, we define C✓g, the velocity-galaxy angular cross- Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use - But we are` working on teasing out anynoise systematics ratio (SNR) of now.EG marginalized over angular scale power spectrum, to be and redshift, given by where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 We nowg translategg these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus, E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 We begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- r r 2c Cˆ tracer-CMB lensing (b)publicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightings within each redshift sample. Also, in order gular quantities, we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to RedshiftEGgg(`, z¯)= space distortions, (1/b)(12) tracer-tracer clustering (b*b) 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and C` as 3H0 (1 +z ¯)C ` turbations, although velocityestimate perturbations given in tend the to staypublic Planck CMB lensing map. wherez ¯ is the average redshift of the galaxy sample. Cg 2 g 2 ` 2 linear atgg smaller2 scalesThe than total for density number perturbations. of galaxies (or quasars) within each is the [ galaxy-convergenceEG(`, z¯)] Due angular to( Ccanceling` cross-power) of spectrum, (galaxy) biasWe expect(parameter,C` ) these e↵ects to be small and will neglect them givenWhy on small does2 scales it= usingmatter the Limber thatg approximation we+ use CMB by + lensingin ourgg forecasts. instead(17). ofsample galaxy along with the survey area are listed in Table 1. EG " C` this probe is bias free.C ` # 2 ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` 4. FORECASTS C` = d W ()fg()Itg hasP 2( very)g little,z (13) ,dependence 2 r In this section we willfrom predict Samushia the ability et of al. current (2014) to set b[CMASS]=2.16 and The- Dramatically uncertaintyZ1 increase in C` can the be z-range written✓ ◆ asof the tracers you can use on the astrophysical relationshipand future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where- wefg isknow the galaxy the( redshiftC z gof)2 distributionCMB+(C lensing+ andNW (exactly)()=Cgg +tween N(nogg GR)photo-z and MG models.needed)sample In all have⇠ our not forecasts been we measured will model-independently for (1 /2CMB)gbetween is the CMB` galaxy lensing kernel. `and the In order` underlying to` assume matter GR when density calculating uncertainties. We describe match- no the intrinsic( kernelC` )= in the alignment galaxy-convergence of CMB power spec- , (18) DR11, so we assume a 10% measurement of and, as in (2` + 1)fsky the sensitivity of the measured EG with the signal-to- trum, we define C✓g, the velocity-galaxy angular cross- Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use - But we are` working on teasing out anynoise systematics ratio (SNR) of now.EG marginalized over angular scale power spectrum, to be and redshift, given by where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 We nowg translategg these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus, E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 We begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- r r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightings within each redshift sample. Also, in order gular quantities, we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and C` as 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g estimate given in the public Planck CMB lensing map. where2 z ¯ is the average redshift of theg galaxy2 sample. C` 2 linear atgg smaller2 scales than for density perturbations. is the [ galaxy-convergenceEG(`, z¯)] angular(C` cross-power) spectrum,() We expect(C` ) these e↵ectsThe to be totalsmall and number will neglect of them galaxies (or quasars) within each givenWhy on small does2 scales it= usingmatter the Limber thatg approximation we+ use CMB by + lensingin ourgg forecasts. instead(17). ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` 4. FORECASTS C` = d W ()fg()g P 2( )g ,z (13), 2 r In this section we willfrom predict Samushia the ability et of al. current (2014) to set b[CMASS]=2.16 and The- Dramatically uncertaintyZ1 increase in C` can the be z-range written✓ ◆ asof the tracers you can use and future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where- wefg isknow the galaxy the( redshiftC z gof)2 distributionCMB+(C lensing+ andNW (exactly)()=Cgg +tween N(nogg GR)photo-z and MG models.needed)sample In all have⇠ our not forecasts been we measured will model-independently for (1 /2CMB)g is the CMB` lensing kernel.` In order` to` assume GR when calculating uncertainties. We describe match- no the intrinsic( kernelC` )= in the alignment galaxy-convergence of CMB power spec- , (18) DR11, so we assume a 10% measurement of and, as in (2` + 1)fsky the sensitivity of the measured EG with the signal-to- trum, we define C✓g, the velocity-galaxy angular cross- Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use - But we are` working on teasing out anynoise systematics ratio (SNR) of now.EG marginalized over angular scale power spectrum, to be and redshift, given by where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 `Note, I am includingsection QSOs with we high quote rms = . Note that for the follow- LSSTC d f () (z)Pgg ,z ` ' 2 We nowg translate theseenough densityinto for clusteringing limits, measurementsf(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set WFIRST W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the Euclid shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus,DES E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 lensing Lens populationWe begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- SDSS rIV r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightingslensing within Source each population redshift sample. Also, in order gularSDSS quantities, I-III we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and0C` as 13H0 (1 +z2 ¯)C 3 4 1100 ` turbations, although velocityestimate perturbations given in tend the to staypublic Planck CMB lensing map. wherez ¯ is the average redshift of the galaxy sample.RedshiftCg 2[E (`, z¯)] (Cg) 2 () ` 2 linear(C atgg smaller) 2 scalesThe than total for density number perturbations. of galaxies (or quasars) within each is the galaxy-convergenceG = angular` cross-power+ spectrum, + We expect` these(17) e↵.ects to be small and will neglect them givenWhy on small does2 scales it usingmatter the Limber thatg approximation we use CMB by lensingin ourgg forecasts. instead ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ 4.ForFORECASTS CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` C` = d W ()fg()g P 2( )g ,z (13), from Samushia et al. (2014) to set b[CMASS]=2.16 and The uncertainty2 in C canr be written as In this section we will predict the ability of current - DramaticallyZ 1 increase` the z-range✓ ◆ of the tracers you can use and future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where fg is the galaxy redshiftg 2 distribution and W()=gg tweengg GR and MG models. In all⇠ our forecasts we will (1- we/ 2know)g is thethe( CMBC z` of) lensing CMB+(C kernel.` lensing+ InN order` )(exactlyC to` + N(no) photo-z needed)sample have not been measured model-independently for CMB(C )= assume GR, (18) when calculating uncertainties. We describe match the kernel` in the galaxy-convergence power spec- the sensitivity of the measuredDR11, soE wewith assume the signal-to- a 10% measurement of and, as in - no intrinsic✓g alignment of(2 `CMB+ 1)f sky G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of ETojeiroG marginalized et al. over (2014), angular we scale assume b[LOWZ]=1.85. We use power- But spectrum, we are to be working on teasing out anyand systematics redshift, given bynow. where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- LSSTC d f () (z)Pgg ,z ` ' 2 We nowg translate these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set WFIRST W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the Euclid shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus,DES E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 lensing Lens populationWe begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- SDSS rIV r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightingslensing within Source each population redshift sample. Also, in order gularSDSS quantities, I-III we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and0C` as 13H0 (1 +z2 ¯)C 3 4 1100 ` turbations, although velocityestimate perturbations given in tend the to staypublic Planck CMB lensing map. wherez ¯ is the average redshift of the galaxy sample.RedshiftCg 2[E (`, z¯)] (Cg) 2 () ` 2 linear(C atgg smaller) 2 scalesThe than total for density number perturbations. of galaxies (or quasars) within each is the galaxy-convergenceG = angular` cross-power+ spectrum, + We expect` these(17) e↵.ects to be small and will neglect them givenWhy on small does2 scales it usingmatter the Limber thatg approximation we use CMB by lensingin ourgg forecasts. instead ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ 4.ForFORECASTS CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` C` = d W ()fg()g P 2( )g ,z (13), from Samushia et al. (2014) to set b[CMASS]=2.16 and The uncertainty2 in C canr be written as In this section we will predict the ability of current - DramaticallyZ 1 increase` the z-range✓ ◆ of the tracers you can use and future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where fg is the galaxy redshiftg 2 distribution and W()=gg tweengg GR and MG models. In all⇠ our forecasts we will (1- we/ 2know)g is thethe( CMBC z` of) lensing CMB+(C kernel.` lensing+ InN order` )(exactlyC to` + N(no) photo-z needed)sample have not been measured model-independently for CMB(C )= assume GR, (18) when calculating uncertainties. We describe match the kernel` in the galaxy-convergence power spec- the sensitivity of the measuredDR11, soE wewith assume the signal-to- a 10% measurement of and, as in - no intrinsic✓g alignment of(2 `CMB+ 1)f sky G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of ETojeiroG marginalized et al. over (2014), angular we scale assume b[LOWZ]=1.85. We use power- But spectrum, we are to be working on teasing out anyand systematics redshift, given bynow. where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- LSSTC d f () (z)Pgg ,z Note, I am including QSOs ` ' 2 We nowg translate these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set WFIRST W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the Euclid shot noise. gg 2 ˆ Peak of the CMB lensing kernel overlap c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 significantlyˆ with allfrom near the current/future true value due to several surveys reasons similar to Thus,DES E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 We begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- SDSS rIV r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightings within each redshift sample. Also, in order gularSDSS quantities, I-III we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and0C` as 13H0 (1 +z2 ¯)C 3 4 1100 ` turbations, although velocityestimate perturbations given in tend the to staypublic Planck CMB lensing map. wherez ¯ is the average redshift of the galaxy sample.RedshiftCg 2[E (`, z¯)] (Cg) 2 () ` 2 linear(C atgg smaller) 2 scalesThe than total for density number perturbations. of galaxies (or quasars) within each is the galaxy-convergenceG = angular` cross-power+ spectrum, + We expect` these(17) e↵.ects to be small and will neglect them givenWhy on small does2 scales it usingmatter the Limber thatg approximation we use CMB by lensingin ourgg forecasts. instead ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ 4.ForFORECASTS CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` C` = d W ()fg()g P 2( )g ,z (13), from Samushia et al. (2014) to set b[CMASS]=2.16 and The uncertainty2 in C canr be written as In this section we will predict the ability of current - DramaticallyZ 1 increase` the z-range✓ ◆ of the tracers you can use and future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where fg is the galaxy redshiftg 2 distribution and W()=gg tweengg GR and MG models. In all⇠ our forecasts we will (1- we/ 2know)g is thethe( CMBC z` of) lensing CMB+(C kernel.` lensing+ InN order` )(exactlyC to` + N(no) photo-z needed)sample have not been measured model-independently for CMB(C )= assume GR, (18) when calculating uncertainties. We describe match the kernel` in the galaxy-convergence power spec- the sensitivity of the measuredDR11, soE wewith assume the signal-to- a 10% measurement of and, as in - no intrinsic✓g alignment of(2 `CMB+ 1)f sky G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of ETojeiroG marginalized et al. over (2014), angular we scale assume b[LOWZ]=1.85. We use power- But spectrum, we are to be working on teasing out anyand systematics redshift, given bynow. where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- LSSTC d f () (z)Pgg ,z ` ' 2 We nowg translate these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set WFIRST W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the Euclid shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus,DES E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 lensing Lens populationWe begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- SDSS rIV r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightingslensing within Source each population redshift sample. Also, in order gularSDSS quantities, I-III we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and0C` as 13H0 (1 +z2 ¯)C 3 4 1100 ` turbations, although velocityestimate perturbations given in tend the to staypublic Planck CMB lensing map. wherez ¯ is the average redshift of the galaxy sample.RedshiftCg 2[E (`, z¯)] (Cg) 2 () ` 2 linear(C atgg smaller) 2 scalesThe than total for density number perturbations. of galaxies (or quasars) within each is the galaxy-convergenceG = angular` cross-power+ spectrum, + We expect` these(17) e↵.ects to be small and will neglect them givenWhy on small does2 scales it usingmatter the Limber thatg approximation we use CMB by lensingin ourgg forecasts. instead ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ 4.ForFORECASTS CMASS, we use the measurements of b8 and f8 lensingg 1 (aka. Reyes et2 al. 2010)?` C` = d W ()fg()g P 2( )g ,z (13), from Samushia et al. (2014) to set b[CMASS]=2.16 and The uncertainty2 in C canr be written as In this section we will predict the ability of current - DramaticallyZ 1 increase` the z-range✓ ◆ of the tracers you can use and future surveys to measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where fg is the galaxy redshiftg 2 distribution and W()=gg tweengg GR and MG models. In all⇠ our forecasts we will (1- we/ 2know)g is thethe( CMBC z` of) lensing source+(C kernel.` +plane InN order` )(exactlyC to` + N(no) photo-z needed)sample have not been measured model-independently for CMB(C )= assume GR, (18) when calculating uncertainties. We describe match the kernel` in the galaxy-convergence power spec- the sensitivity of the measuredDR11, soE wewith assume the signal-to- a 10% measurement of and, as in - no intrinsic✓g alignment of(2 `CMB+ 1)f sky G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of ETojeiroG marginalized et al. over (2014), angular we scale assume b[LOWZ]=1.85. We use power- But spectrum, we are to be working on teasing out anyand systematics redshift, given bynow. where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 We nowg translategg these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus, E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 We begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- r r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightings within each redshift sample. Also, in order gular quantities, we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and C` as 3H0 (1 +z ¯)C ` turbations, although velocityestimate perturbations given in tend the to staypublic Planck CMB lensing map. wherez ¯ is the average redshift of the galaxy sample. Cg 2[E (`, z¯)] (Cg) 2 () ` 2 linear(C atgg smaller) 2 scalesThe than total for density number perturbations. of galaxies (or quasars) within each is the galaxy-convergenceG = angular` cross-power+ spectrum, + We expect` these(17) e↵.ects to be small and will neglect them givenWhy on small does2 scales it usingmatter the Limber thatg approximation we use CMB by lensingin ourgg forecasts. instead ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 g 1 2 ` 4. FORECASTS lensing (aka. Reyes et al.2 2010)? C` = d W ()fg()g P ( )g ,z (13), 2 r In this section we willfrom predict Samushia the ability et of al. current (2014) to set b[CMASS]=2.16 and The uncertaintyZ1 in C` can be written✓ ◆ as - Dramatically increase the z-range of the tracersand future you surveys can to use measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where fg is the galaxy redshiftg 2 distribution and W()=gg tweengg GR and MG models. In all⇠ our forecasts we will (1- we/ 2know)g is the the ( CMBzC of` )CMB lensing+( C kernel.lensing` + InN exactly order` )(C to` (no+ N photo-z) needed)sample have not been measured model-independently for CMB(C )= assume GR, (18) when calculating uncertainties. We describe match the kernel` in the galaxy-convergence power spec- the sensitivity of the measuredDR11, soE wewith assume the signal-to- a 10% measurement of and, as in - not much astrophysical✓g systematics(2` + 1)fsky in CMB lensing (vs galaxy lensing)G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of ETojeiroG marginalized et al. over (2014), angular we scale assume b[LOWZ]=1.85. We use power- But spectrum, we are to beworking on teasing out any systematicsand redshift, givennow. by where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS 4

Starting with Eq. 1, EG can be estimated in terms of noise in the convergence power spectrum computed using power spectra as the formalism in Hu & Okamoto (2002), and N gg is the shot noise. 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased Eˆ (k, z)= r , (11) G G 2 3H (1 + z)Pˆ✓g(k) from the true value due to several reasons similar to 0 those outlined in the Appendix of Reyes et al. (2010). 2 where P 2( )g is the galaxy- ( ) cross-power For one, the lensing kernel and galaxy redshift distribu- r r spectrum and P✓g is the galaxy-peculiar velocity cross- tions are not constants, requiring us to account for the power spectrum. Projecting 3D power spectra into an- weightings within each redshift sample. Also, in order gular quantities, we can estimate EG as to extend our measurement of EG to small scales, we must correct for the scale-dependence of the bias due 2 ˆg c C` to clustering at nonlinear scales. We may also need to EˆG(`, z¯)= , (12) 2 ˆ✓g consider scale-dependent due to nonlinear velocity per- 3H0 (1 +z ¯)C ` turbations, although velocity perturbations tend to stay g wherez ¯ is the average redshift of the galaxy sample. C` linear at smaller scales than for density perturbations. is the galaxy-convergence angular cross-power spectrum, We expect these e↵ects to be small and will neglect them given on small scales using the Limber approximation by in our forecasts.

2 g 1 2 ` 4. FORECASTS C` = d W ()fg() P 2( )g ,z (13), 2 r In this section we will predict the ability of current Z1 ✓ ◆ and future surveys to measure EG and di↵erentiate be- where fg is the galaxy redshift distribution and W ()= tween GR and MG models. In all our forecasts we will (1 / ) is the CMB lensing kernel. In order to CMB assume GR when calculating uncertainties. We describe match the kernel in the galaxy-convergence power spec- the sensitivity of the measured E with the signal-to- ✓g G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of EG marginalized over angular scale power spectrum, to be and redshift, given by

2 GR 2 ✓g 1 2 ` 2 [EG (zi)] C = d W ()f () P ,z . (14) ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the It is no man’s land2 out there ... 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 We nowg translategg these into ing limits, f(R) gravity is set to its upper limit value 4 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)observables(¯z) gg that we can measure: ⇥ Starting with Eq. 1, EG can beC estimated, in terms of noise in the(15) convergenceof power parameters spectrum computed is B0 =0 using.4, 1 =1.2, and s = 4, unless power spectra' as 2 ` the formalism in Hu &otherwise Okamoto (2002), stated. and N gg is the shot noise. gg 2 ˆ c P 2( )g(k) A precise measurement of E will be slightly biased where CEˆ` (k,is z)= the galaxyr angular, auto-power(11) spectrum. G 4.1. Current Surveys G 2 ˆ from the true value due to several reasons similar to Thus, E in this3H case(1 + canz)P✓ beg(k) written as G 0 those outlined in the Appendix of Reyes et al. (2010). 2 We begin with forecasts of EG measurements from the where P 2( )g is the galaxy- ( )2 cross-powerg For one, the lensing kernel and galaxy redshift distribu- r r 2c Cˆ tracer-CMB lensingpublicly available Planck CMB lensing map (Planck Col- spectrum andˆ P✓g is the galaxy-peculiar velocity` cross- tions are not constants, requiring us to account for the power spectrum.EG(` Projecting, z¯)= 3D power spectra into an- gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆweightings within each redshift sample. Also, in order gular quantities, we can estimate0 EG as to` extend our measurementtroscopic of EG galaxyto small samples scales, we from BOSS DR11 (Anderson must correct for the scale-dependence of the bias due 2 ˆg et al. 2014), as well as the spectroscopic quasar (QSO) and we canˆ write thec errorC` of EG in terms ofto the clustering errors at nonlinear scales. We may also need to EGgg(`, z¯Redshift)= space, distortions(12) tracer-tracer clustering 2 ˆ✓g consider scale-dependentsample due to (Pˆaris nonlinear et velocity al. 2014) per- from DR11. We use the noise of and C` as 3H0 (1 +z ¯)C ` turbations, although velocityestimate perturbations given in tend the to staypublic Planck CMB lensing map. wherez ¯ is the average redshift of the galaxy sample. Cg 2[E (`, z¯)] (Cg) 2 () ` 2 linear(C atgg smaller) 2 scalesThe than total for density number perturbations. of galaxies (or quasars) within each is the galaxy-convergenceG = angular` cross-power+ spectrum, + We expect` these(17) e↵.ects to be small and will neglect them givenWhy on small does2 scales it usingmatter the Limber thatg approximation we use CMB by lensingin ourgg forecasts. instead ofsample galaxy along with the survey area are listed in Table 1. EG " C` C` # 2 ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 g 1 2 ` 4. FORECASTS lensing (Reyes et al. 2010)?2 C` = d W ()fg()g P ( )g ,z (13), 2 r In this section we willfrom predict Samushia the ability et of al. current (2014) to set b[CMASS]=2.16 and The uncertaintyZ1 in C` can be written✓ ◆ as - Dramatically increase the z-range of the tracersand future you surveys can to use measure()/EG and10%. di↵erentiate The corresponding be- values for the LOWZ where fg is the galaxy redshiftg 2 distribution and W()=gg tweengg GR and MG models. In all⇠ our forecasts we will (1- we/ 2know)g is the the ( CMBzC of` )CMB lensing+( C kernel.lensing` + InN exactly order` )(C to` (no+ N photo-z) needed)sample have not been measured model-independently for CMB(C )= assume GR, (18) when calculating uncertainties. We describe match the kernel` in the galaxy-convergence power spec- the sensitivity of the measuredDR11, soE wewith assume the signal-to- a 10% measurement of and, as in - not much astrophysical✓g systematics(2` + 1)fsky in CMB lensing (vs galaxy lensing)G trum, we define C` , the velocity-galaxy angular cross- noise ratio (SNR) of ETojeiroG marginalized et al. over (2014), angular we scale assume b[LOWZ]=1.85. We use power- But spectrum, we are to beworking on teasing out any systematicsand redshift, givennow. by where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam- Shirley Ho, Sapetime 2Odyssey, Stockholm 2015  GR 2 computed✓g 1 from CAMB (Lewis2 ` et al. 2000), N is the 2 ples.[ ForEG ( thezi)] BOSS quasar sample, we use the BOSS C = d W ()f () P ,z . (14) ` ` g ✓g SNR (EG)= 2 , (19) 2 1 [EG(`,zi)] Z ✓ ◆ `,zi X This cross-power spectrum is a construct used to measure where zi denotes redshift bins. We also calculate the EG without multiplicative bias, and is not equivalent to 2 value between GR and MG models to determine if the RSD angular power spectrum derived in Padmanab- a particular EG measurement could distinguish between han et al. (2007). GR and a given MG model. We write 2 as In our analysis, as in Reyes et al. (2010), we assume MG GR 2 that the RSD parameter will be measured separately, 2 [EG (`,zi) EG (zi)] and we approximate the lensing kernel, the redshift dis- (EG)= 2 , (20) [EG(`,zi)] tribution, and as constants over redshift within the X`,zi integral. Also, we assume from linear theory ✓ = f.In MG where EG (`,zi)istheEG estimate for a given MG that case, Eq. 14 can be written as model, which is generally `-dependent. Throughout the 2 2 ✓g W (¯) 2 2 ` section we quote rms = . Note that for the follow- C d f () (z)P ,z ` ' 2 g gg ing limits, f(R) gravity is set to its upper limit value 1 5 p Z ✓ ◆ B0 =5.6 10 , and that chameleon gravity’s base set W (¯)(¯z) gg ⇥ C , (15) of parameters is B0 =0.4, 1 =1.2, and s = 4, unless ' 2 ` otherwise stated. gg where C` is the galaxy angular auto-power spectrum. 4.1. Current Surveys Thus, EG in this case can be written as We begin with forecasts of EG measurements from the 2 ˆg publicly available Planck CMB lensing map (Planck Col- ˆ 2c C` EG(`, z¯)= gg , (16) laboration et al. 2014) and the CMASS and LOWZ spec- 3H2(1 +z ¯)W (¯)(¯z)Cˆ 0 ` troscopic galaxy samples from BOSS DR11 (Anderson and we can write the error of EG in terms of the errors et al. 2014), as well as the spectroscopic quasar (QSO) gg sample (Pˆaris et al. 2014) from DR11. We use the noise of and C` as estimate given in the public Planck CMB lensing map. 2 g 2 2 gg 2 [EG(`, z¯)] (C` ) () (C` ) The total number of galaxies (or quasars) within each 2 = g + + gg (17). sample along with the survey area are listed in Table 1. EG " C` C` # ✓ ◆ ✓ ◆ ✓ ◆ For CMASS, we use the measurements of b8 and f8 The uncertainty in Cg can be written as from Samushia et al. (2014) to set b[CMASS]=2.16 and ` ()/ 10%. The corresponding values for the LOWZ (Cg)2 +(C + N )(Cgg + N gg) sample have⇠ not been measured model-independently for 2(Cg)= ` ` ` ` , (18) ` (2` + 1)f DR11, so we assume a 10% measurement of and, as in sky Tojeiro et al. (2014), we assume b[LOWZ]=1.85. We use  where C` , the convergence auto-power spectrum, is Eq. 17 to calculate the EG uncertainty for these sam-  computed from CAMB (Lewis et al. 2000), N` is the ples. For the BOSS quasar sample, we use the BOSS Can6 we use this new probe with BOSS ?

Table 2 Properties of the Advanced ACTPol CMB survey. Note that the 2 area of the survey is 20,000 deg and we assume P = T p2. a Center Freq. T (µK-arcmin) ✓res (arcmin) 90 GHz 7.8 2.2 150 GHz 6.9 1.3 230 GHz 25 0.9

aper resolved pixel EG overlaps with only 75% of DESI’s area; we take this into account in our DESI⇠ forecasts. For Euclid and WFIRST ELGs, we assume b(z)=0.9+0.4z, a fit (Takada et al. 2014) to semi-analytic models (Orsi et al. 2010) that com- pares well with data. We determine the redshift distri- bution of Euclid H↵ galaxies using the H↵ luminosity function from Colbert et al. (2013) and assume a flux 16 limit of 4 10 . This flux limit is in the middle of the redshift (z) Pullen, Alam & Ho, 2015range being⇥ considered, so the following Euclid forecasts Figure 3. EG forecasts for BOSS galaxy surveys cross-correlated can change accordingly. We also assume a 3% error in with the current Planck CMB lensing map, in comparison with the within z =0.1 bins for Euclid and WFIRST (Amen- latest measurement of EG using galaxy-galaxy lensing (Reyes et al. 2010). Note that we do not translate their EG measurement from dola et al. 2013). For all subsequent forecasts, we assume the WMAP3 (Spergel et al. 2007) to the cosmology we EG measurements over angular scales 100 ` 500. Shirley Ho, Sapetime Odyssey,assume. Stockholm The 2015 band around the GR prediction corresponds to the The forecasts are listed in Table 3, but here we list likelihood function of EG based on Planck and BOSS constraints some highlights. Figs. 4 and 5 show that DESI and on cosmological parameters. The EG predictions for f(R)gravity and chameleon gravity are averaged over the wavenumber range Euclid combined with Planck can each measure EG al- at every redshift corresponding to 100 < ` < 500, the range used most at the 2% level, unlike WFIRST which is limited for CMASS. The dashed lines show chameleon gravity predictions by its small survey area. This should allow DESI and for higher and lower values of 1.Thesesurveysarenotsensi- tive enough to tighten constraints on f(R)gravitysetbycurrent Euclid combined with Planck to produce constraints of measurements. some models, and 1 constraints should get tighter than those from BOSS. For Adv. ACTPol, DESI should reach ity to chameleon gravity is only slightly better, in that a 1% measurement of EG, allowing it to di↵erentiate GR CMASS, LOWZ, and BOSS QSOs together could di↵er- and chameleon gravity with 1 > 1.1 at the 5 level. entiate models with very high (or low) values of 1 from DESI produces tighter constraints than Euclid due to its GR due to the rapid evolution of EG with 1. higher number density at low redshifts. Note that we use a moderate number of redshift slices for each sur- 4.2. Upcoming Spectroscopic Surveys vey, as seen in Figs. 4 and 5. The redshift accuracy of We now consider upcoming spectroscopic surveys. We these spectroscopic surveys would allow us to use much consider two cases for the CMB lensing map, including smaller redshift bins in order to decrease errors in EG. (1) the full Planck CMB lensing map and (2) the Ad- But each of these surveys are shot-noise dominated on vanced ACTPol2 CMB lensing map. In both cases, we the scales where the EG signal dominates, increasing the assume the CMB lensing maps will be estimated using errors in the galaxy-CMB lensing cross-correlation. We the temperature map and both E and B polarization also considered more pessimistic errors in , finding that maps, and we assume the B map only contains noise. We increasing the error in by a factor of 3 did not notice- predict the noise in the Planck lensing map assuming the ably increase EG errors from Planck, while it increased detector sensitivity and beam sizes listed in the Planck EG errors from Adv. ACTPol by less than 2%. Bluebook (The Planck Collaboration 2006). Advanced ACTPol will survey 20,000 deg2, and its increased tem- 4.3. Upcoming Photometric Surveys perature and polarization sensitivity will create a CMB In this section we consider measuring EG from upcom- lensing map that is an order of magnitude more sensitive ing photometric galaxy surveys. These surveys, which than Planck. The specifications we use for Adv. ACT- measure less precise redshifts than spectroscopic surveys, Pol are listed in Table 2. For spectroscopic surveys, we are tailored for measuring weak lensing and not RSD. consider the DESI emission line galaxy (ELG), luminous However, the errors in EG are dominated by the CMB red galaxy (LRG), and quasar surveys, as well as the lensing at lower redshifts where the EG signal is highest, Euclid H↵ survey and the WFIRST H↵ and OIII com- meaning that reducing shot noise in the lensing-galaxy bined survey. The properties of the surveys are listed cross-correlation through attaining higher number densi- in Table 1. For DESI, we assume the same values as in ties is be more important than having precise redshifts. 3 the DESI Conceptual Design Report : bLRGD(z)=1.7, Also, upcoming photometric surveys plan to approach bELGD(z)=0.84, bQSOD(z)=1.2, where D(z)isthe redshift precisions of z/(1 + z) 0.05. Recent work has growth factor. We also assume a 4% error in within shown that upcoming photometric⇠ surveys could mea- z =0.1 bins. Note that Adv. ACTPol’s survey area sure RSD (Ross et al. 2011; Crocce et al. 2011; Asorey et al. 2014). This may cause photometric surveys to pro- 2 private communication with Advanced ACTPol team duce competitive EG measurements. It should be noted 3 http://desi.lbl.gov/cdr/ that Adv. ACTPol gets close to the lensing noise limit We probe a complimentary range of scales when compared to using galaxy-lensing instead of CMB-lensing

EG

R (Mpc/h) Reyes et al. 2010

Shirley Ho, Sapetime Odyssey, Stockholm 2015 We start from 30 Mpc/h and have significant signals to larger scales.

BOSS X Planck Lensing can probe up to ~100 Mpc//h

EG

R (Mpc/h) Reyes et al. 2010

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Preliminary look into BOSS X Planck-lensing

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Preliminary look into BOSS X Planck-lensing

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Preliminary look into BOSS X Planck-lensing

Shirley Ho, Sapetime Odyssey, Stockholm 2015 LARGER SCALES SMALLER SCALES R (Mpc/h)

Two following Reyes et al.’s largest scale measurement EG Slides removed

Shirley Ho, Sapetime Odyssey, Stockholm 2015 l (angular scales) Pullen, Alam & Ho, preliminary

Figure 2: Test of GR using EG measurements. Observed EG measurements using galaxy-CMB

lensing and galaxy clustering with 1 errors using the CMASS galaxy sample and the Planck CMB

lensing map. The horizontal axes are described in the caption for figure (1). We show estimates

using jackknife resampling of the full sample [green crosses; see figure (1)] and estimates using

the full sample with errors computed from 100 CMASS mock galaxy catalogues and Gaussian

simulations of the lensing convergence field (red crosses). The blue line shows the GR prediction

E =0.402 0.012 with the error denoted by the shaded blue region and determined from the G ± likelihood from Planck and BOSS measurements. The turquoise line shows the f(R) gravity upper

20 limit prediction from the parameter B0 proportional to the f(R) curvature today. The shaded

24 purple region shows the EG-space of chameleon9 gravity with parameters B0 =0.4, s =4, and

the range =0.8 1.6. The shaded orange region shows the same but for =0.7 0.8, which 1 1 is disfavored by our measurement at over 99% confidence. Conclusion

» 1) BAO has come of age, we can make 1% distance measurement using BAO at multiple redshifts • 2) This allows us to make quantitative statement of our cosmology AND • 3) There are many interesting fronts in LSS that we can work on, and one of them is to think very hard about what we can do with the cross-correlations with current and upcoming CMB experiments and what they provide.

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Conclusion

» 1) BAO has come of age, we can make 1% distance measurement using BAO at multiple redshifts • 2) This allows us to make quantitative statement of our cosmology AND • 3) There are many interesting fronts in LSS that we can work on, and one of them Correlations Galaxy is to think very hard about what we can do with the cross-correlations with current and upcoming CMB experiments and what they provide.

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Conclusion

» 1) BAO has come of age, we can make 1% distance measurement using BAO at multiple redshifts • 2) This allows us to make quantitative statement of our cosmology AND • 3) There are many interesting fronts in LSS that we can work on, and one of them is to think very hard about what we can do with the cross-correlations with current and upcoming CMB experiments and what they provide.

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Conclusion

» 1) BAO has come of age, we can make 1% distance measurement using BAO at multiple redshifts • 2) This allows us to make quantitative statement of our cosmology AND • 3) There are many interesting fronts in LSS that we can work on, and one of them is to think very hard about what we can do with the cross-correlations with current and upcoming CMB experiments and what they provide.

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Conclusion

» 1) BAO has come of age, we can make 1% distance measurement using BAO at multiple redshifts • 2) This allows us to make quantitative statement of our cosmology AND • 3) There are many interesting fronts in LSS that we can work on, and one of them is to think very hard about what we can do with the cross-correlations with current and upcoming CMB experiments and what they provide.

Shirley Ho, Sapetime Odyssey, Stockholm 2015 Conclusion

» 1) BAO has come of age, we can make 1% distance measurement using BAO at multiple redshifts • 2) This allows us to make quantitative statement of our cosmology AND • 3) There are many interesting fronts in LSS that we can work on, and one of them is to think very hard about what we can do with the cross-correlations with current and upcoming CMB experiments and what they provide.

Shirley Ho, Sapetime Odyssey, Stockholm 2015