Neutrino Masses with Lensing of the Cosmic Microwave Background

(Study of Experimental Probe of Inﬂationary Cosmology)

Asantha Cooray University of California-Irvine (almost) uniform 2.726K blackbody (Penzias & Wilson)

Universe at 400kyr: the microwave sky

COBE (Mather & Smoot) O(10-5) perturbations (+galaxy) Dipole (local motion)

WMAP Anisotropies

Around 2013 with Planck

Hu & Dodelson Amblard

Hu Lensing distributes anisotropies from degree scales to damping tail and smooths acoustic peaks

In temperature hard to see because of other secondaries

In polarization lensing mixes E & B modes. Polarization secondaries are smaller. Non-Gaussianity of lensing Bad: decreases information content of lensing B-modes from the case of a simple Gaussian mode counting. (Beware of Gaussian Fisher predictions of B-modes)

Good: allows a statistical mechanism to reconstruct foreground mass distribution responsible for lensing 4

FIG. 1: The correlation matrix [Eq. (25)] for temerature (left), E-mode (middle), and B-mode (right) power spectra between different l values. The color axis is on a log scale and each scale is different for each panel. As is clear from this figure, the off diagonal correlation is weak for both θ and E-mode power spectra, but is more than 0.1formostentriesfortheB-mode power spectrum. This clearly shows that the non-Gaussianities are most pronounced for the B-mode signal and will impact the information extraction from the angular power spectrum of B-modes than under the Gaussian variance alone. The B-mode covariance shown in the left panel agrees with Figure 5 of Ref.[14].

mm1m2 mm1m2m3 where the expressions for the mode coupling integrals +2Ill1l2 and +2Jll1l2l3 are described in Refs. [15, 16]. As for the covariance of E-mode powerspectrum, we write

1 1 ˜ ˜∗ ˜ ˜∗ ˜E ˜E CovEE El1m1 El1m1 El2m2 El2m2 Cl1 Cl2 = + +( + )δl1 l2 (14) ≡ 2l1 +12l2 +1 " #− H I J K m1m2 ! where

1 φ E 2 E 2 l1+l2+L = CL (2Fl1Ll2 Cl2 ) +(2Fl2Ll1 Cl1 ) (1 + ( 1) ) H (2l1 +1)(2l2 +1) − L ! " # 2 φ E E l1+L+l2 = CLCl1 Cl2 (1 + ( 1) )2Fl1Ll2 2Fl2Ll1 I (2l1 +1)(2l2 +1) − !L ! 2 φ E E l1+L+l 2 ! ! = 2 CLCl Cl1 (1 + ( 1) )(2Fl1Ll ) J (2l1 +1) ! − !L,l (l1(l1 +1) 4) φ E 2 = − CL(Cl1 ) L(L +1)(2L +1). (15) K − 2π(2l1 +1) !L The last two terms can be written in terms of the lensed power spectrum of E-mode anisotropies as

2 ˜E 2 + = (Cl1 ) , (16) J K 2l1 +1 where 1 ( F )2 C˜E =[1 (l2 + l 4)R]CE + Cφ 2 ll1 l2 CE(1 + ( 1)l+l1+l2 ) l − − l 2 l1 2l +1 l2 − !l1l2 1 R = l (l +1)(2l +1)Cφ 8π 1 1 1 l1 !l1 1 (2l +1)(2l1 +1)(2l2 +1) ll l F = [l (l +1)+l (l +1) l(l +1)] 1 2 . (17) 2 ll1 l2 2 1 1 2 2 − 4π 20 2 $ % − & ˜E Note that Cl is the power spectrum of the lensed E-modes. CMB lens reconstructionNon-Gaussianity of lensing

Lensing weakly correlates CMB modes with l = l :

T (l)T (l)∗ φ(l l). ∝ − Reconstructed ﬁeld φ is quadratic in CMB temperature:

a φ(n)= ∂ α(n)∂aβ(n) d2l 1 α(n)= T (l)eil n 2 TT TT · (2π) C + N b 2 TT d l C il n β(n)= 2 TT TT T (l)e · (2π) C + N b Second idea for detecting CMB lensing: look for extra power in φ. Compute C φφ: quadratic in φ, or four-point in CMB. WMAP3: statistical errors only give 1σ. (> 50 publications) In addition, systematics likely to be difficult. . . Pipeline PipelineHint of lensing in WMAP? Final result (including systematic errors) Start Cross-correlation3.4σ detection, as (step a cross-correlation 8): (1) ❄ Gaussian fieldsStartg , φ , aunlensedLens reconstructionInput: Lensing (step potential 6): and galaxy (1) m m m (2) ❄{ } fields (shown bandlimited to 20 ❄ unlensed Input: Maximum likelihood CMB Gaussian fields glensedm, φm, a(4)m ≤ Combine statistical errors with sys- Lensed(2) CMB{am } map 40): ❄(3) ≤ tematic errors considered previ- ❄lensed (4) ❄ Lensed CMB am (3) ously: ❄ ❄ WMAP beam effects φg Output: Cross correlation C , Galactic CMB foregrounds WMAP data NVSS data (5) Output:withReconstructed estimator normalization lensing po- and Point sources + SZ WMAP data❄ NVSS data(7) (5) ❄ tentialstatisticalφ (shown errors bandlimited computed to by Filtered❄ CMB am (7) (6) Filtered galaxy Filtered CMB❄am ❄ 20 Monte 40): Carlo (6) Filteredfield galaxygm ≤ ≤ Reconstructed❄ field✁gm 2 Toφg assess total statistical significance:7 fit to one large bandpower Reconstructedpotential φm ✁ ✁ C = (33.2 10.5) φg 10− potential φ ❅ in multiple of fiducial± C× . m ✁(8)✁ (20 40, stat.) ❅ (8)✁❅❅❘ ✁☛ φg Lensing❅❅❘ estimator✁☛ C Result: 1.15 0.≤34,≤ i.e. a 3.4σ detection, consistent with the φg ± Lensing estimator C fiducial model. Smith et al. 07 no detection limits on lensing-ISW and lensing-SZ Calabrese et al. 09 Next steps

A detection of the lensing potential power spectrum with WMAP-7? Requires a computation of the 4 point function, work started, results out soon!!! (Joseph Smidt et al. in preparation)

Existing estimators (Hu & Okamoto; Seljak & Hirata) are biased, need to properly account for the Gaussian part of the trispectrum and remove noise bias.

Fast, optimized estimators for non-Gaussianity now developed in a series of papers by Munshi, Smidt et al. (we measured the primordial trispectrum for the ﬁrst time ever in 1001.5026)

Still requires a large number of Monte-Carlo simulations. Limited by computational resources. Out to ell of 900, ~25,000 CPU hours. Naive estimator scales as l4. Fast estimators scales as l3logl. CMB lensing

CMB lensing vs. galaxy lensing

Advantages:

1. A precisely known source 2. Linear fluctuations, there is really no need to model non- linearities down to sub-percent precision. 3. Community experience in analyses of complex CMB datasets

Disadvantages:

Finite information content! Experimental Probe of Inflationary Cosmology

EPIC Selected by NASA in 2003 for a 2 to 3-year study, again in 2008-2009 In 2008-2009, EPIC was put forward as a general CMB community-supported mission concept for the CMBpol post-Planck mission. In Europe, B-POL study (but not selected; Euclid selected for dark energy as a Cosmic Visions M class mission).

Jamie Bock (JPL), PI

Bock et al. 0906.1188 Post-Planck Mission Effort in US

The EPIC-IM Study Team PPPDT CMB Inflation Probe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participants O&**/6(9>%1/B( ,-. L/6=(4*M+6( E4?K Decad al Whi te P apers 8*&#(,>'6B>6( 23(8/*D/%/H –The Origin of the Universe as Revealed Through the Polarization of the CMB, Dodelson et al. 8*+&6(L/&=+6N( 23(?&6(7+/N> and 211 Co-signers, ArXiv 0903.3796 3'&>T.+6(L$> ?=&6Q>*#(2: –Observing the Evolution of the Universe, Page et al. and 168 Co-signers, ArXiv 0903.0902 !#*+&6(.//( 23(8/*D/%/H –A Program of Technology Development and Sub-Orbital Observations of CMB Polarization !6#*/M(.&6N/( 3&%=/<'G,-. Leadinggg to and Including a Satellite Mission,,y Meyer et al. and 141 Co-signers 3'&*%/B(.&M*/6 E&=/(;+%%/*( 23(?&6(7+/N> –Theory and Foregrounds: 5 Papers with 135 Authors and Co-Authors 9+/6 EN$H/6( ,-. – Probing Inflation with CMB Polarization, Baumann et al. 2008, ArXiv 0811.3919 U%/6&(-+/*C&>%+ 2?3 – Gravitational Lensing, Smith et al. 2008, ArXiv 0811.3916 E+<>%&B(->6='+/$ 4!?@(A*&6$CCN(-$N/=( 4!?@(A*&66( 23?7 –Path to CMBPol: Conference on CMBPol mission in July with 104 participants 9$&6 K*&6( 23(8/*D/%/HG??. Mission Studyyp Reports 8==O+%%+8*/==(O+%%+&1B( ,-. ,>6&B(S1$+#P+6&B 3&%=/<'G,-. –Study of the EPIC-Intermediate Mission, Bock et al. 2009, ArXiv 0906.1188 –The Experimental Probe of Inflationary Cosmology, Bock et al. 2008, ArXiv 0805.4207 See http://cmbpol.uchicago.edu for a full compilation V Observational Cosmology - University of Minnesota Richness of the CMB Polarization Landscape

!"!$%&'($)"*+,#$) &-$./('+)/,).,&+0.) 1%(0%2.$)/,)#%+-023) /%04 ! 5($.0&0,2) .,&+,4,36 ! 8$-%(/'($)9(,+)&.%4$)021: ! ;$0,20<%/0,2 =0&/,(6

!$%&'($)7*+,#$) .,&+0.)&=$%() &-$./('+)/,).,&+0.)) 40+0/& ! >$'/(02,)+%&&)=0$(%(.=6 ! 8%(@)$2$(36)%/)<)A)B

!%-)?%4%./0.) +%32$/0.)90$4#&)10%) #'&/) -,4%(0<%/0,2 ! DE)%2#)4%(3$*&.%4$)7*90$4#

!$%&'($)C294%/0,2%(6) ! ?FG)$2$(36)&.%4$ 7*+,#$)&-$./('+)%/) ! H%(3$)90$4#)0294%/0,2

()I)J:JK)/,)%&/(,-=6&0.%4) ! 2/ L)().,2&0&/$2.6)/$&/ 40+0/&

Observational Cosmology - University of Minnesota Precision Cosmology

Observational Cosmology - University of Minnesota Mapping NASA Objectives to EPIC Instrument Requirements

NASA NASA Measurement Instrument Research Targeted Outcome* Criteria Criteria Objective* _ All-sky coverage Measure inflationary _ w -1/2 < 6 µK- B-mode power p arcmin EPIC-low cost Test the Inflation spectrum to _ 30 – 300 GHz hypothesis of the Big astrophysical limits for _ 1˚ resolution just for this Bang 2 < _ < 200 at r = 0.01 _ Control systematic after foreground errors below r = removal What are the 0.01 origin, Precisely determine Measure EE to cosmic evolution, and the cosmological variance into the Silk fate of the parameters governing damping tail to probe _ 10' resolution universe? the evolution of the primordial density universe perturbations Improve our knowledge of dark energy, the EPIC-IM optimized mysterious cosmic energy for the goal of that will determine the Measure lensing-BB to fate of the universe -1/2 cosmic limits to probe _ wp < 2 µK- measuring CMB Investigate the seeds of neutrino physics and arcmin cosmic structure in the early (z~2) dark lensing with cosmic microwave energy density and _ 6' resolution background equation of state deliverables of Measure the distribution of dark neutrino masses. How do planets, matter in the universe stars, galaxies and cosmic structures Determine the mechanism(s) by which Measure EE to cosmic come into being? _ Primary mission most of the matter of the variance to distinguish parameters above universe became reionization histories reionized Map Galactic magnetic Study the birth of stellar _ 500 and 850 GHz fields via dust and planetary systems bands polarization *Taken from NASA 2007 Science Plan Primary Objective

Secondary Objective Optimizing an experiment for a science goal Particle physics application of EPIC

CMB lensing probes linear fluctuations Source properties known (Both these lead to systematic errors in galaxy lensing)

Lensing B-modes and CMB Cosmic Shear Reconstruction

A deliverable: neutrino mass (Σmν < 0.05 eV or better at 95% confidence level)

Test SuperK Atmosphere oscillations that suggest 2 -3 2 Δmν ∼ 2x10 eV and distinguish between two mass hierarchies

EPIC study reports NeutrinoNeutrino mass hierarchy Masses from cosmology

ForObservational the LCDM cosmological Cosmology model, - University EPIC, as currently of Minnesota configured, reaches a sum of the neutrino masses of 0.042 eV and if the equation of state of dark energy is allowed to vary this constraint is at 0.047eV at the same 95% confidence level. This is not a simple Gaussian Fisher matrix estimate. It accounts for the full covariance, part of which was based on simulations. EPIC-IM Specification Sheet

)*+,-.( !"#$%&"'( /%,012+3*41%, /%,012+3*41%,

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ass similar to the Planck satellite mission Observational Cosmology - University of Minnesota EPIC-IM Mission Concept Experimental Probe of Inflationary Cosmology – Intermediate Mission (Bock, JPL)

!"#$%$&'())*+$,'-.(/* 0*1*)2(3* !"#$%&'()%*+(%+,#-$'"#+&#*$)*.-*/+01,%/#$+(%+2%$,)2+&),)($ !3)/#+456+7%"+$#*$)()8)(9 ! !"#$%"!&'()&*("+$&+,$-(,.!"/.- 4-'.*$5(2-1$61-/* !:).:+$#*$)()8)(9+7%"+;*7&-()%*-"9+<1,%/#$ ! .01&*.-$*"$2344$5!&+67$8(--("+-9 ! 3)/#+7"#='#*29 + 2%8#"-.#+ 7%"+ 7%"#."%'*/$ !:).:+7"#='#*2)#$+7%"+>-&-2()2+$2)#*2#

&((17/.$)8)9*% 4:$;-1($<'=79 !?-@),-&+'$#+%7+A-$$)8#+2%%&)*. ! -6&+$-*'&*.:;$ <"'$ !&':.=-6&!.$ %"!&'()&*("+ !#@("#,#&9+$(-M&#+(:#",-&+#*8)"%*,#*( !077)2)#*(+B+C+2"9%2%%&#"DE?;F;G ! $'*$:)#&/+$),)&-"+(%+K&-*2L+-*/+NOPQ !H%*()*'%'$+IJJ+,C2%%&#"+DEK&-*2LG ! -(8%!.$"%.'&*("+->$6"+?.+*("+&!$-%&6.6'&<*

@((!**A5!7*!!(*((@&--$-(8(!&'$*"$*A.$5!&+67$-&*.!!(*.$8(--("+

Observational Cosmology - University of Minnesota Highly Redundant & Uniform Scan Coverage

N-hits (1-day) Angular Uniformity* (6-months)

Planck

WMAP

EPIC

0 1 *2 + 2 High Throughput, Multi-Band Focal Plane

! DF G@9FF@.< ! 1H#I G@99JFKLM@NNLO@7/E#4P >4,0-?@ !"#$ T 1 6 89:; A@9B;@ GD ! Q44@,"#@734,"/(,I/30@P#0P/I/R#@ !*'+ 234 7 7/E %&'() %,"-./0) %5) %P<8=) C" %0<) 2343.#I#"P 89:; 67 ! KS,0HPK@S,0HP ;X XL 9L WNF XW ! Z0-4TH/0V@NFFJ@XNF@&'(@[3"@ WF &,4,-I/-@HTPI@.,77/0V LN 9K WYL NBO WNF WL

+T-U@4,"V#"@IU"3TVU7TI@,0H@P#0P/I/R/IC@IU,0@@,0C@ OF 9; 9WW; ;BN WXF 9N 74,00#H@PT283"2/I,4@#E7#"/.#0I 9FF XBL ;9KY 9BX 9FF 9F "#$%& 9NF NBY WFLX 9BL XF X

;;F WBX 9;KY ;BN 9WF 9N

WLF ;BN OLL NBY LFF WW

NFF 9BO 9FK; 9Y

XNF 9BF KWX OLF

D3I,4 99FKL FBK NL NBL

WF@&'( \/[#I/.#@]@L@C#,"P LN@&'( XNF@&'( 13/P#@.,"V/0]@9BL OF@ &'( 500 GHz 9FF@&'( WLF@&'( ;;F@&'( 9NF@&'(

Observational Cosmology - University of Minnesota ‘Moore’s Law’ for Sensitivity and Mapping Speed

BLIP – CMB Ground

BLIP – CMB Space ! # " /'(/"3 ,-./,01 %&'#'()* + 2 $ 6

45 ACT BICEP2 EBEX SCUBA2 !"

!"! Observational Cosmology - University of Minnesota Neutrino mass hierarchy from cosmology Neutrino Masses Can we do better? Further optimize EPIC (at a very high cost), factor of 1.2 to 1.3 at most improvement with CMB polarization alone

Better, Combine EPIC with Euclid/JDEM-WL for a factor of ~2 to 3 improvement through z-binned lensing + a good model for non-linearities for galaxy lensing.

Observational Cosmology - University of Minnesota lensing of 21-cm: highly futuristic Summary

• Planck should do BB lensing, and get down to ~0.2 eV level

• Post-Planck EPIC satellite for CMB polarization is well developed.

• US-based CMB community has requested NASA to start a project ofﬁce after the 2010 Astronomy Decadal Survey, based on recommendations on CMB sciences.

• If started, EPIC phase-A to begin around 2015, launch around 2020-2021.

• Will Planck provide a hint of tensors and/or primordial non- Gaussianity? motivation for EPIC will be clearer then.