Cosmology with the SKA

Chris Blake (Swinburne) Science Cartoons Plus -- The Cartoons of S. Harris 09/27/2006 01:06 PM

S. Harris Astronomy Cartoons TheOur darkcurrent energy model puzzle of cosmology Page 1 | Page 2 | Page 3

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We have a superbly detailed • picture of the early Universe [e.g. CMB, nucleosynthesis]

• We have a model for the evolution of the Universe that matches a range of

cosmological data Copyright © 2006 by Sidney Harris. No reproduction other than for personal enjoyment without written permission.

• This model invokes 3 new pieces of physics : inflation, dark matter and dark energy

http://www.sciencecartoonsplus.com/galastro2c.htm Page 1 of 1 Dark energy : is it vacuum energy?

A cosmological constant matches the data so far, but its amplitude is inexplicable Cosmology : the optimistic viewpoint !

• Dark matter and energy show that our understanding of physics is incomplete • Astronomy can provide fundamental physical insights into quantum theory, gravity, and particle physics • We are working in the breakthrough era where new data should be revolutionary! Large-scale structure

• Geometrical information (e.g. baryon acoustic oscillations)

• Gravitational information (e.g. redshift-space distortions)

• Primordial information (e.g. shape of large-scale power spectrum) TheCosmology dark energy with thepuzzle SKA • 2004 style ...

Cosmology with the SKA C.A. Blakea,F.B.Abdallab,S.L.Bridlec,S.Rawlingsb aSchool of Physics, University of New South Wales, Sydney, NSW2052,Australia bAstrophysics, Department of Physics, University of Oxford,KebleRoad,Oxford,OX13RH,UK cDepartment of Physics and Astronomy, University College London, London, WC1E 6BT, UK

We argue that the Square Kilometre Array has the potential to make both redshift (HI) surveys and radio continuum surveys that will revolutionize cosmological studies, provided that it has sufficient instantaneous field- of-view that these surveys can cover a hemisphere (fsky 0.5) in a timescale 1yr.Adoptingthisassumption, ∼ ∼ we focus on two key experiments which will yield fundamental new measurements in cosmology, characterizing the properties of the mysterious dark energy which dominatesthedynamicsoftoday’sUniverse.ExperimentI 9 will map out 10 (fsky/0.5) HI galaxies to redshift z 1.5, providing the premier measurement of the clustering ∼ ≈ power spectrum of galaxies: accurately delineating the acoustic oscillations and the ‘turnover’. Experiment II will 10 quantify the cosmic shear distortion of 10 (fsky/0.5) radio continuum sources, determining a precise power ∼ spectrum of the dark matter, and its growth as a function of cosmic epoch. We contrast the performance of the SKA in precision cosmology with that of other facilities which will, probably or possibly, be available on a similar timescale. We conclude that data from the SKA will yield transformational science as the direct result of four key features: (i) the immense cosmic volumes probed, exceeding future optical redshift surveys by more than an order of magnitude; (ii) well-controlled systematiceffects such as the narrow ‘k-space window function’ for Experiment I and the accurately-known ‘point-spread function’ (synthesized beam) for Experiment II; (iii) the ability to measure with high precision large-scale modesintheclusteringpowerspectra,forwhichnuisance effects such as non-linear structure growth, peculiar velocities and ‘galaxy bias’ are minimised; and (iv) different degeneracies between key parameters to those which are inherent in the Cosmic Microwave Background.

1. Background cosmic expansion is described by the Hubble pa- arXiv:astro-ph/0409278v1 13 Sep 2004 −1 −1 rameter h = H0/(100 km s Mpc ). Structures Over the last few years we have entered an in the Universe are assumed to grow by gravita- ‘era of precision cosmology’ in which rough esti- tional amplification of a primordial ‘power spec- mates of many of the key cosmological parameters trum of fluctuations’ created by inflation, which have been replaced by what can reasonably be de- is taken to be a ‘scale free’ power law Pprim(k) ∝ scribed as ‘measurements’ (parameters known to k nscalar .1 better than ∼ 10 per cent accuracy). Remarkable Within this framework, we begin by reviewing progress in observations of the temperature fluc- what the CMB tells us about the cosmological tuations in the Cosmic Microwave Background model. The basic CMB observable is the angu- (CMB) has been central to this scientific transfor- lar power spectrum of temperature fluctuations, mation (e.g. the recent results from the WMAP which consists of a series of ‘acoustic peaks’. We satellite, Spergel et al. 2003). note that the physics of the CMB fluctuations (i.e. The current standard cosmological model

(‘ΛCDM’) assumes that the Universe is composed 1 of baryons, cold dark matter (CDM) and Ein- Apowerlawfunctionis‘scalefree’becauseitcontainsno preferred length scale. The power law index nscalar =1 stein’s cosmological constant Λ. The present-day is described as ‘scale invariant’ because in this case, the densities of baryons, (baryons + CDM) and Λ,as matter distribution has the same degree of inhomogeneity afractionofthecriticaldensity,aredenotedby on every resolution scale (is ‘self-similar’). Inflationary theories of the early Universe predict that this should be Ωb, Ωm and ΩΛ,respectively.Thelocalrateof approximately true.

1 Cosmology with the SKA • 2015 style ...

Cosmology with the SKA – overview

1,2 3,4 5,1 1,6 Roy Maartens⇤ , Filipe B. Abdalla , Matt Jarvis , Mario G. Santos – on behalf of the SKA Cosmology SWG 1 Department of Physics, University of Western Cape, Cape Town 7535, South Africa 2Institute of Cosmology & Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK 3Department of Physics & Astronomy, University College London, London WC1E 6BT, UK 4Department of Physics & Electronics, Rhodes University, Grahamstown 6140, South Africa 5Astrophysics, University of Oxford, Oxford OX1 3RH, UK 6SKA South Africa, The Park, Park Road, Cape Town 7405, South Africa

E-mail: [email protected]

The new frontier of cosmology will be led by three-dimensional surveys of the large-scale struc- ture of the Universe. Based on its all-sky surveys and redshift depth, the SKA is destined to revolutionize cosmology, in combination with future optical/ infrared surveys such as Euclid and LSST. Furthermore, we will not have to wait for the full deployment of the SKA in order to see transformational science. In the first phase of deployment (SKA1), all-sky HI intensity mapping surveys and all-sky continuum surveys are forecast to be at the forefront on the major questions of cosmology. We give a broad overview of the major contributions predicted for the SKA. The SKA will not only deliver precision cosmology – it will also probe the foundations of the standard model and open the door to new discoveries on large-scale features of the Universe. arXiv:1501.04076v1 [astro-ph.CO] 16 Jan 2015

Advancing Astrophysics with the Square Kilometre Array June 8-13, 2014 Giardini Naxos, Italy

⇤Speaker.

c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ Cosmology with the SKA

• Use HI intensity mapping to measure large-scale structure across large volumes to high redshift

• Test cosmology with cross-correlations of the radio continuum survey with CMB and optical surveys

• Measure weak gravitational lensing in radio continuum observations using new techniques

• Constrain primordial non-Gaussianity using the largest-scale modes Upcoming optical surveys

Euclid TheHI intensity dark energy mapping puzzle • 21cm surveys which do not detect individual galaxies but the integrated emission21 CM BRIGHTNESS in each FLUCTUATIONS pixel of a datacube 3

GBT 15hr field (800.4 MHz, z = 0.775) GBT 15hr field, cleaned, beam convolved (800.4 MHz, z = 0.775)

0.6 1000 3 3 0.4

2.5 500 2.5 0.2

2 0 2 0 Dec Dec

-0.2 1.5 1.5 -500 Temperature (mK) Temperature (mK) -0.4 1 1 -1000 -0.6

220 219.5 219 218.5 218 217.5 217 216.5 216 215.5 4 220 219.5 219 218.5 218 217.5 217 216.5 216 215.5Masui, Switzer, et. al. RA RA 1 fluctuations. This is required for forecasts of the sensitivity of 15 hr future 21 cm intensity mapping experiments. Since r<1 we Figure 1. Maps of the GBT 15 hr field at approximately the band-center. The purple circle is the FWHM1 hr of the GBT beam, and the color rangesaturatesin -3 have put a lower limit on ΩHIbHI. some places in each map. Left: The raw map as produced by the map-maker. It is dominated by synchrotronΩ b emission r = 0.43 10 from both extragalactic point sources and smoother emission from the galaxy. Right: The raw map with 20 foreground modes removed per line ofHI sightHI relative to 256 spectral bins, as described in To determine ΩHI alone from our cross-correlation requires Sec. 3.2. The map edges have visibly higher noise or missing data due to the sparsity of scanning0.1 coverage. The cleaned map is dominated by thermal noise, andexternal estimates of the H I bias and stochasticity. The linear we have convolved by GBT’s beam shape to bring out the noise on relevant scales. bias of H I is expected to be ∼ 0.65 to ∼ 1 at these redshifts (Mar´ın et al. 2010; Khandai et al. 2011). Simulations to inter-

In addition to the observed maps, we develop signal-only (mK) The foreground filter is built from the real map which has a simulations based on Gaussian realizations of the non-linear, 2 limited number of independent angular elements. This causeprets Chang et al. (2010) find values for r between 0.9 and 0.95 (k) (Khandai et al. 2011), albeit for a different optical galaxy pop- redshift-space power spectrum using the empirical-NL model Δ the 0.01 transfer function to have components in both the angular described by Blake et al. (2011). and frequency direction (Nityananda 2010), with the angulaulation.r Measurements of the correlation coefficient between part dominating. This is accounted for in our transfer func-WiggleZ galaxies and the total matter field are consistent with unity in this k-range (with r ! 0.8)(Blakeetal.2011). Chang3.2. From et maps al. to power(2008) spectra tion. Subtleties of the cleaning method will be described in a m,opt 0.001 These suggest that our cross-correlation can be interpretedas future methods paper. × −3 × −3 The approachMasui to 21 cmet foreground al. (2013) subtraction in literature ΩHI between 0.45 10 and 0.75 10 . has been dominated by the notion of fitting and subtracting We estimate the 0.1 errors and their covariance in our cross- Measurements with Sloan Digital Sky Survey power spectrum by calculating the-1 cross-power of the cleaned smooth, orthogonalpolynomialsalong each line of sight. This k (h Mpc ) (Prochaska and Wolfe 2009) suggest that before z =2, ΩHI is motivated by the eigenvectors of smooth synchrotron fore- GBT maps with 100 random catalogs drawn from the Wig-may have already reached ∼ 0.4 × 10−3.Atlowredshift, gleZ selection function (Blake et al. 2010). The mean of these ∼ ± × −3 grounds (Liu and Tegmark 2011, 2012). In practice, instru- Figure 2. Cross-power between the 15hr and 1hr GBT fields and WiggleZ. 21 cm measurements give ΩHI(z 0) = (0.43 0.03) 10 mental factors such as the spectral calibration (and its stabil- Negativecross points powers are shown is withconsistent reversed with sign and zero, a thin as line. expected.The solid line The vari-(Martin et al. 2010). Intermediate redshifts are more dif- ity) and polarization response translate into foregrounds that is the meanance of accounts simulations for based shot on noise the empirical-NL in the galaxy model of catalogBlake et and al. vari-ficult to measure, and estimates based on Mg-II lines have more complex structure. One way to quantify this struc- (2011)ance processed in the by the radio samemap pipeline. either from real signal (sample vari-in DLA systems observed with Hubble Space Telescope −3 ture is to use the map itself to build the foreground model. ance), residual foregrounds or noise. Estimating the errorsinfind ΩHI(z ∼ 1) ≈ (0.97 ± 0.36) × 10 (Rao et al. ≈ To do this, we find the frequency-frequencycovariance across spectrumthis way is then requires given many by P independentHI,opt(k)= modesTbbHIb toopt enterrPδδ each(k) spec-2006), in rough agreement with z 0.2 DLA measure- the sample of angular pixels in the map, using a noise inverse wheretralPδδ cross-power(k) is the matter bin. power This fails spectrum. at the lowest k values and soments (Meiring et al. 2011) and 21 cm stacking (Lah et al. weight. We then find the principal components along the fre- Thethese large-scale scales are matter discarded. power spectrum In going fromis well-known the two-dimension from al2007). This is in some tension with a model where ΩHI quency direction, order these by their singular value, and sub- CMBpower measurements to the 1D (Komatsu powers presented et al. 2011) here, and we the weight bias of each the 2D kfalls- monotonically from the era of maximum star forma- 2 ± tract a fixed number of modes of the largest covariance from opticalcell galaxy by the population inverse variance is measured of the to 2D be cross-powerbopt =1.48 across thetion rate (Duffy et al. 2012). Under the assumption that 0.08 setat the of mock central galaxy redshift catalogs. of our survey The 2D (Blake to 1D et binning al. 2011). weight isbHI =0.8,r =1,thecross-correlationmeasurementhere each line of sight. Because the foregrounds dominate the real ∼ × −3 map, they also dominate the largest modes of the covariance. Simulationsmultiplied including by the nonlinear square of scales the beam (as inand Sec. foreground 3.1) are clean-suggests ΩHI 0.5 10 ,inbetteragreement,butclearly There is an optimum in the number of foregroundmodes to run throughing transfer the same functions. pipeline Fig. as 2 the shows data. the We resulting fit the galaxy-H un- betterI measurements of bHI and r are needed. Redshift space distortions can be exploited to break the degeneracy between remove. For too few modes, the errors are large due to resid- knowncross-power prefactor Ω spectra.HIbHIr of the theory to the measured cross- ± Ω and bias to measure these quantities independently of ual foreground variance. For too many modes, 21 cm signal powers shown in Fig. 2, and determine ΩHIbHIr = [0.44 HI 4. RESULTS−3 AND DISCUSSION simulations (Wyithe 2008; Masui et al. 2010). This will be is lost, and so after compensating based on simulated signal 0.10(stat.) ± 0.04(sys.)] × 10 for the 15 hr field data, and Ω b Tor = relate [0.41 the± 0. measured11(stat.) ± spectra0.04(sys with.)] theory,× 10−3 wefor thestart withthe subject of future work. loss (see below), the errors increase modestly. We find that HI HI Our measurement is limited by both the number of galaxies removing 20 modes in both the 15 hr and 1 hr field maximizes 1hrfielddata.the mean 21 Thesystematictermrepresentsthe cm emission brightness temperature9% (Changabso- et al. lute calibration2010), uncertainty from Sec. 3.1. It does not include in the WiggleZ fields and by the noise in our radio observa- the signal. Fig. 1 shows the foreground-cleaned 15 hr field tions. Simulations indicate that the variance observed in our map. current uncertainties in the cosmological parameters1 or in the1 −3 − 2 2 radio maps after foreground subtraction is roughly consistent We estimate the cross-power spectrum using the inverse WiggleZ bias, butΩ theseHI areΩm sub-dominant.+(1+z) Ω CombiningΛ 1+ the twoz Tb =0.29 ± ± × mKwith. the expected levels from thermal noise. This is perhaps noise variance of the maps and the WiggleZ selection function fields yields ΩHI10bHI−3r != [0.43 00.37.07(stat.) " 0.04(sys! 1.8.)] " −1 not surprising, our survey being relatively wide and shallow as the weight for the radio and optical survey data, respec- 10−3.Thesefitsarebasedontherange0.075 hMpc < (1) −1 compared to an optimal LSS survey, however, this is nonethe- tively. The variance is estimated in the mapping step and rep- k

Cosmology with SKA HI• IM surveysGreat potential owingMario to G. Santos the volume probed! Cosmology with the SKA Roy Maartens BAO distance/expansion measurements:

Cosmology with SKA HI IM surveys Mario G. Santos Figure 4: Survey volumes and redshift range for various current and future surveys (volume calculated at the central redshift). Dark energy measurements:

DA(z), as functions of redshift, as has been done successfully with recent large galaxy redshift surveys such as BOSS and WiggleZ. Measuring these functions is vital for testing theories of dark energy which seek to explain the apparent acceleration of the cosmic expansion, as they constrain its equation of state, w = P/r, and thus its physical properties. Shedding light on the behaviour of dark energy – especially whether w deviates from 1 and whether it varies in time – is one of the foremost problems in cosmology. To precisely measure the BAO feature in the matter correlation function, which appears as a ‘bump’ at comoving separations of r 100h 1 Mpc, one needs to detect many galaxies (in order ⇡ to reduce shot noise), and to cover as large a survey volume as possible (in order to reduce sample variance). Intensity mapping has a few major advantages over conventional galaxy surveys for this task. IM surveys can map a substantial fraction of the sky with low angular resolution in a Figure 1: Error on the Hubble rate and angularBull diameter et distanceal. (2014) from radial and transverse BAO measure- short period of time. Combined with the wide bandwidths of modern radio receivers,ments, this showing makes performance of SKA HI surveys – intensity mapping (IM) and galaxy redshift surveys (gal). it possible to cover extremely large survey volumes and redshift ranges in a relativelyEuclid short spectroscopic time, survey shown for comparison. (Bull et al. 2014) helping to beat down sample variance (see Fig. 4). While individual galaxies cannot in general be resolved, each telescope pointing measures the Figure 6: Left: Predicted constraints from SKA on dynamical dark energy parameters. We show predicted integrated emission from many galaxies, making the total signal easier to detect and reducingThere are the CMB constraints on the low redshift Universe, principally via the lensing of the constraints from SKA1 IM and SKA2 galaxy, compared with predictions for Euclid. Right: Predicted shot noise. All that is required is to obtain sufficient flux sensitivity to detect theCMB integrated by large-scale 21cm structure. The CMB can also contribute through cross-correlation with large- emission and to haveconstraints sufficient resolution from SKA to resolve on the the unparameterized required scales at a growthgiven redshift.scale function structure Figuref s data,58 from in the the form SKA1 of the (galaxy integrated and Sachs-Wolfe IM) and effect. However, the main probe summarises the expectedthe SKA2 constraints galaxy from survey, the SKA compared HI IM surveys with for predicted two relevant constraints targetof the scales: low-redshift coming the Universe from the – Euclid and especially galaxy of survey. the critical Both question of the late-time acceleration BAO scale at k 0.074 Mpc 1 and a very large scale, past the equality peak at k 0.01 Mpc 1.We ⇠ constraints include Planck+BOSS priors. ⇠ of the Universe – is the large-scale distribution of matter (together with SNIa surveys). Galaxy see the huge constraining power of these surveys. In particular, due to the large volumessurveys have probed, not reached the levels of precision of the CMB. But major advances have been made, they will be unmatched7.2Growth on ultra-large of structure scales. Even at BAO scales, both SKA1-MIDespecially and in SUR measurements of the BAO scale. present constraints not far from Euclid while only using a 2 year survey (the full Euclid requires ⇠ A new frontier of precision cosmology is emerging – three-dimensional surveys of the LSS in about 5 years). Moreover,Viewed SKA1-LOW in redshift will be able space, to make the a detection matter distribution at z 4 which is again anisotropic will due to the distorting effect of ⇠ the Universe. Current galaxy surveys do not yet cover both a wide area of sky and a significant be an unique feature.peculiar velocities in the line of sight direction. Coherentredshift depth. peculiar This is velocities what is needed on forlarge a high scales enough encode volume – and thus a high enough number For the BAO scalesinformation (see Table about1 and Fig. the5 history, left panel), of the angular growth resolution of structureof of modes the Phase in– for the next-generation 1 Universe through precision cosmology. their dependence But future planned surveys, like Euclid, LSST SKA dishes is such that these scales are best matched to an autocorrelation surveyand at low especially redshift, the SKA, will achieve both of these features. These LSS surveys will open up the f (z) on the linear growth rate, , which can be measurednew frontier from of the cosmology degree ofthat anisotropy can deliver precision of the redshift-at and beyond CMB levels. Indeed, the largest space correlation function.17 The growth rate is directly related to the strength of gravity, and so is an extremely useful tool for probing possible deviations from general relativity that have been3 invoked as an alternative to dark energy to explain cosmic acceleration. Intensity mapping and galaxy surveys do not measure the linear growth rate directly, but are instead sensitive to simple combinations of f (z), the bias b(z), and the overall normalisation of the power spectrum s8(z). A reasonable choice of parametrisation is to take the combinations 2 ( f s8,bs8). As shown in Raccanelli et al. (2014), a 10,000 hour and 25,000 deg SKA phase 1 intensity mapping autocorrelation survey will be capable of measuring f s8 with high precision over a wide redshift range, obtaining sub-1% constraints in the range 0.05 . z . 1.0 with Band 2 of SKA1-MID or SUR, and reaching out to z 2.0 with 4% precision using Band 1 of MID/SUR ⇡ ⇠ (see Fig. 6). At low redshifts, these figures are highly complementary to (e.g.) a Euclid galaxy redshift survey, which should obtain 0.5% measurements of f s in the interval 0.7 z 2.0. By com- ⇠ 8 . . parison, SKA1-MID/SUR will have 0.5% measurements for z 0.3–0.7. ⇠ ⇡ 7.3 Probing ultra-large scales As briefly mentioned above, there is important information that can be extracted from the ultra-large scale modes of order and above the cosmological horizon (see Fig. 5, right panel). We refer the reader to Camera et al. (2014) and references therein for an extensive description of the ultra-large scale effects briefly mentioned here, as well as to the ways by which the SKA will be able to tackle successfully the technical problems arising when trying to access those scales.

19 TheHI intensity dark energy mapping puzzle • Challenges : enormous foreground subtraction problem, including polarization leakage

• Need realistic simulations!

See Laura’s talk ... TheContinuum dark energy surveys puzzle : cross-correlations • Radio continuum surveys trace a high-z density map • Expect correlations with CMB (late-time ISW effect and lensing) and low-z galaxies (magnification)

Planck collaboration (2013) TheContinuum dark energy surveys puzzle : late-time ISW effect

Cross-correlation between the NVSS and CMB 8 T. Giannantonio,• R. Crittenden, R. Nichol and A. J. Ross

The significance of the integrated Sachs-Wolfe effect revisited 9

g = −1 Catalogue A ± σA S/N expected S/N g = −0.25 g =0 g =+0.25 g =+1 ≥ 2× 2MASS cut 1.40 ± 2.09 0.70.5 SDSS gal DR8 1.24 ± 0.57 2.21.6 SDSS LRG DR7 2.10 ± 0.84 2.51.2

Figure 3. Updated results of the cross-correlation of all the data setswiththeWMAP7ILCmap.Mostdata(darkgreen,solid)areingood agreement with the 6 theoretical predictions for a ΛCDM model (red, short-dashed), with the only exception of theLRGswhichshowanexcessat>1-σ level. The highly correlatedNVSS 1.21 ±20.4310 2.82.6 error bars are from 5000 Monte Carlo mocks and are 1-σ,exceptfor2MASSwheretheyare0.5-σ to improve readability of the plot. Further, the first fiveHEAO data 1.37 ± 0.56× 2.42.0 points for 2MASS have been excluded due to potentialNolta contamination byet the SZ effect.al. The(2004) light-green, long-dashed lines show the previously published2 data by G08, and the blue, dot-dashed lines are the best amplitude fits. ± . 0.65 2.0 Ho et al. (2008) ∼ SDSS QSO DR6 1.43 0.62 2 31.7 By analytically maximising the likelihood, we obtain that the best ± . ± . ! . < . Giannantoniovalue etA and al. its variance (2013) for each catalogue are: TOTAL 1.38 0.32 4 4 0 4 3 1, 7 6 p −1 Tg p −1 C giwˆ i, j=1 ij j 2 −1 A = , σ = C gig j , (11) ! p C−1g g A  ij  i, j=1 ij i j i%, j=1 Table 2. Results from the updated data set compared with the expected   !   Tg signal-to-noise calculated using Eq. (6) for each catalogue. The first five wherew ˆ i are the observed CCF for each survey (sampled in = p 13 angular bins) and Cij is the measured covariancedatapoints matrix of for 2MASS have been excluded. For the total expected S/N,we dimension p described above. To obtain an unbiased estimator of −1 the inverse covariance Cij ,wecorrecttheresultobtainedbyinvert-show both the value estimated from the MC mocks (see below), and using ing Cij by a factor α = (N − p − 2)/(N − 1) (Hartlap et al. 2007); however in our case (for N = 5000 realisations)the this upper correction limit of Eq. (5). We estimate a ∼ 0.4 σ systematic error on the is negligibly small. This method can be immediatelytotal general signal-to-noiseised ratio, due to possible different masks and other choices to the full case, in which we fit a single amplitude to a template which includes the six CCFs. In this case the totalentering number of angu- into its determination. lar bins, and thus the dimension of the covariance matrix, becomes p = 6 × 13 = 78. The results with this method and the new data are given in Figure 4. Dependence of the results on the different WMAP data releases. Table 2, where we can see that if we identify the signal-to-noise Most results vary little compared with the size of the error bars; the largest = changes can be seen in NVSS, bringing the results closer to the ΛCDM ex- ratio as S/N A/σA,thenthetotalsignificanceofadetectionis pectations. The error bars on 2MASS are again 0.5-σ. now at the 4.4 σ level when a single amplitude is used for all six catalogues. It is worth noticing that our significance estimation is however based on a fiducial model which includes not only the WMAP7 4 !c 2012 RAS, MNRAS 000,1–19 best-fit parameters, but also the assumed redshift distributions and simple bias model of the surveys. While this is reasonable to give an initial estimate of the significance of the detection, a full cosmo- logical analysis should ideally take into account the uncertainties in these quantities, e.g. with the help of additional nuisance param- eters. The assumption of constant biases is especially uncertain, in particular for very deep catalogues like HEAO and NVSS (see e.g. Sch¨afer et al. 2009), and this issue should be addressed in a full cosmological analysis allowing for a more realistic bias evolution. The different assumptions for the biases and for the redshiftdistri- butions may for example explain the difference between our results and those by Ho et al. (2008), where a higher excess signal was found, at the 2 σ level above the ΛCDM predictions. In Table 2 we also compare the1000 results with the expected signal-to-noise calculated using Eq.∼ (6) for each catalogue, and us- ing the upperuv limit of Eq. (5) for the total. We can see that the mea- sured results are higher than the expectations in most cases.Given this discrepancy exists between expectations and observations, we Figure 5. Distribution of the signal-to-noise ratio for our 5000 MC reali- next proceed to quantify its significance by studying the distribu- sations (blue histograms), compared with the observations (red solid lines) and the theoretical expectations (green). The different green lines refer to: ◦ tion of the ISW signal-to-noise obtained using our 5000 mock maps 40 of the galaxy surveys. We show these distributions in Fig. 5: here no shot noise (short-dashed), and shot noise included (long-dashed). The − we can see that they are broad, and the position of the observed S/N top panel shows each catalogue separately, the bottom panel is the full com- is well within the expected scatter. In more detail, we fit a Gaussian bination, for which we also show the best-fit Gaussian distribution and its parameters. to the distribution of the mock total signal-to-noise, wherewefind that the mean (i.e. the expectation for the total S/N from ΛCDM) is 3.05, and the r.m.s. is 1 by construction. This places our observed result 1.35 σ away from the mean. changing the thresholds in the extinction masks, or excluding parts AfurtherinterestingpointtobelearntfromFig.5isthecom- of the data (such as the Southern hemisphere for the new SDSS parison between theoretical S/N with (green solid lines) and with- DR8 galaxies). Another change which is typically at the same level out (green dashed lines) shot noise. We can see that the effectof is produced if we decide to completely discard the pixels nearthe g shot noise is particularly large for the quasars, due to theirlimited edge of the survey, for which the mask weighting is fi < 1, in- number density. From this we conclude that future measurements stead of correcting them with the appropriate weights. Furthermore of extended quasar catalogues have the potential to significantly any extra large-scale power in the auto-correlation functions, which improve the existing results, due to the large redshift coverage of could arise e.g. due to low-redshift contamination or other system- these sources. atics, would increase the variance of the cross-correlations. We dis- Given the number of different assumptions in the method of cuss this below in Section 5.3.2, showing that its effect is limited the analysis, we roughly estimate that a systematic uncertainty of and in agreement with our systematic estimation of 0.4 σ. ! 0.4needstobeincludedonthefinalfigureofthesignal-to-noise We have also checked the effect of removing any one cata- ratio. For example, using other reasonable redshift distributions for logue from the analysis, finding in this case that the total signifi- the catalogues typically results in changes of the signal-to-noise ra- cance can not be lowered below 3.9 σ,whichistheresultobtained tio of the order 0.2 − 0.4. Similar differences are obtained when when ignoring the NVSS data.

!c 2012 RAS, MNRAS 000,1–19 TheContinuum dark energy surveys puzzle : late-time ISW effect • Physical evidence for dark energy

2

Granett et al. (2008) de Putter et al. (2010)

• Problem : limited precision

FIG.1.—Stacked regions on the CMB corresponding to supervoid and supercluster structures identified in the SDSS LRG catalog. We averaged CMB cut-outs around 50 supervoids (left) and 50 superclusters (center), and the combined sample (right). The cut-outs are rotated, to align each structure’s major axis with the vertical direction. Our statistical analysis uses the raw images, but for this figure we smooth them with a Gaussian kernel with FWHM 1.4⇥. Hot and cold spots appear in the cluster and void stacks, respectively, with a characteristic 1 radius of 4⇥, corresponding to spatial scales of 100 h Mpc. The inner circle (4⇥ radius) and equal-area outer ring mark the extent of the compensated filter used in our analysis. Given the uncertainty in void and cluster orientations, small-scale features should be interpreted cautiously. with previous results (Giannantonio et al. 2008), we measured cluster and void lists, we discarded any structures that over- a cross-correlation amplitude between our two data sets on 1 lapped LRG survey holes by 10%, that were 2.5 (the scales of 0.7µK. stripe width) from the footprint⇥ boundary, that were centered To find supervoids in the galaxy sample, we used the on a WMAP point source, or that otherwise fell outside the parameter-free, publicly available ZOBOV (ZOnes Bordering boundaries of the WMAP mask. On Voidness; Neyrinck 2008) algorithm. For each galaxy, We found 631 voids and 2836 clusters above a 2⇥ signifi- ZOBOV estimates the density and set of neighbors using the cance level, evaluated by comparing their density contrasts to parameter-free Voronoi tessellation (Okabe et al. 2000; van de those of voids and clusters in a uniform Poisson point sample. Weygaert & Schaap 2007). Then, around each density mini- There are so many structures because of the high sensitivity mum, ZOBOV finds density depressions, i.e. voids. We used of the Voronoi tessellation. Most of them are spurious, arising VOBOZ (Neyrinck, Gnedin & Hamilton 2005) to detect clus- from discreteness noise. We used only the highest-density- ters, the same algorithm applied to the inverse of the density. contrast structures in our analysis; we discuss the size of our In 2D, if density were represented as height, the density de- sample below. pressions ZOBOV finds would correspond to catchment basins We defined the centers of structures by averaging the posi- (e.g. Platen, van de Weygaert & Jones 2007). Large voids tions of member galaxies, weighting by the Voronoi volume in can include multiple depressions, joined together to form a the case of voids. The mean radius of voids, defined as the av- most-probable extent. This requires judging the significance erage distance of member galaxies from the center, was 2.0; of a depression; for this, we use its density contrast, compar- for clusters, the mean radius was 0.5. The average maximum ing against density contrasts of voids from a uniform Poisson distance between void galaxies and centers was 4.0; for clus- point sample. Most of the voids and clusters in our catalog ters, it was 1.1. For each structure, an orientation and ellip- consist of single depressions. ticity is measured using the moments of the member galaxies, We estimated the density of the galaxy sample in 3D, con- though it is not expected that this morphological information verting redshift to distance according to WMAP5 (Komatsu is significant, given the galaxy sparseness. et al. 2008) cosmological parameters. To correct for the vari- able selection function, we normalized the galaxy densities to 3. IMPRINTS ON THE CMB have the same mean in 100 equally spaced distance bins. This also removes almost all dependence on the redshift-distance Figure 1 shows a stack image built by averaging the regions mapping that the galaxy densities might have. We took many on the CMB surrounding each object. The CMB stack cor- steps to ensure that survey boundaries and holes did not af- responding to supervoids shows a cold spot of -11.3µK with 3.7⇥ significance, while that corresponding to superclusters fect the structures we detected. We put a 1 buffer of galax- ies (sampled at thrice the mean density) around the survey shows a hot spot of 7.9µK with 2.6⇥ significance, assessed footprint, and put buffer galaxies with maximum separation in the same way as for the combined signal, described below. Figure 2 shows a histogram of the signals from each void and 1 from each other in front of and behind the dataset. Any real galaxies with Voronoi neighbors within a buffer were not cluster. used to find structures. We handled survey holes (caused by To assess the significance of our detection, we averaged bright stars, etc.) by filling them with random fake galaxies the negative of the supervoid image with the supercluster im- at the mean density. The hole galaxies comprise about 1/300 age, expecting that the voids would produce an opposite sig- of the galaxies used to find voids and clusters. From the final nal from the clusters. We used a top-hat compensated filter to measure the fluctuations, averaging the mean temperature Continuum surveys : gravitational lensing • Probes total mass distribution and spacetime metric Continuum surveys : gravitational lensing

Detection of cosmic shear in FIRST survey •14 Chang, Refregier & Helfand

Weak Lensing by Large-Scale Structure withChangFIRST et al. (2004) 15

zero at the selected angular scales, we add the B-mode covariance to the E-mode covariance matrix. As a result, the covariance matrix accounts for all the sources of er- rors, namely, intrinsic source shapes, shape measurement errors, cosmic variance, and systematics. The data points from angular scales 200! < θ < 1000! are partially degenerate and contain only 3-4 indepen- dent measurements. We therefore use a singular value 1 decomposition to calculate W− ,anddiscardthesin- gular values of W which are negligible compared to the rest. Since the Map data vector was initially computed at small angular intervals, we only keep four data points which contain the highest signal-to-noise ratios and are independent. The redshift distribution of our sample is rather un- certain, as indicated by the various models for the ra- dio source redshift-distribution discussed in 3.2. We § therefore chose to vary two parameters in our fit: σ8, the mass power spectrum normalization in spheres of 1 8h− Mpc, and zm,themediansourceredshift.Weas- sumed a ΛCDM model with fixed values of Ωm =0.3 and Γ =0.21. Note that, although we are probing scales 1 Fig. 16.— Constraints on the spectrum normalization, σ8, greater than 8h− Mpc, the parameter σ8 is convenient Fig. 13.— Map statistics as a function of aperture radiusandθ.The on the sourceFig. median 14.— redshift,Samezm as,fromourFIRSTcosmic the previous figure, but the Map statistics fortop comparing panel shows our results the E-mode with those variance from! otherM 2 ", groups while theshear bottom measurement.are computed The solid using lines indicate the simulations, the 68% and which 95% serve as a null test. and methods. ap M 2 CL from FIRST, excluding the predominantly low-redshift objects Thepanel resulting shows theχ2 contour B-mode plot variance is shown! ⊥ in".Thecurvesindicatepre- Fig. 16. The with APM optical counterparts. The dashed lines are the 68% dictions from the Ω =0.3 ΛCDM model, with σ8 =0.9, Γ =0.21, solid contours indicatem the 68.3%, 95.4% confidence levels CL from FIRST including sources with the APM counterparts. A and several source median redshifts zm. ΛCDM model with Ωm =0.3andΓ =0.21 was assumed. Also from FIRST, excluding the predominantly low-redshift shown for comparison is the constraint from the WMAP CMB objects with APM optical counterparts. For comparison, experiment σ8 =0.9 ± 0.1 (68%CL; Spergel et al. 2003). the dashed contours show the 68.3% CL constraint from the FIRSTIn order sources to test including for the those presence with the of APM a lensing coun- signal on terparts which, as expected, are consistent with lower zm scales larger than 50!,weremovedFIRSTsourcesfor values.which As an a check, optical we counterpart used the linear could power be spectrum identified inWe the have presented our cosmic shear measurement us- and the fitting formula from Smith et al. (2003) and ing the FIRST Radio Survey over 8,000 square degrees PeacockAPM & catalog Dodds (1996), (McMahon and found & Irwin the contours 1992), do which not amountsof sky. We apply the shear measurement method de- varyto appreciably. 10% of the This FIRST is expected sample. since Excluding we are probing quasars,scribed which in Chang & Refregier (2002) to measure shear theare linear both part rare of the and mass mostly power point spectrum. sources To a (all good of whichdirectly are in Fourier space, where interferometric data are approximation,excluded from the contours our source (excluding sample), APM the counter- redshiftscollected. of the In this shapelets approach, we carefully deter- parts)APM correspond sources to peak at around z 0.15 and are formined the the input parameters for the source shape decom- . most part boundedzm 0 6 by z ! 0.3(McMahonetal.2002).∼ position, and verified that the shear estimators are un- σ8 0.95 0.22, (37) biased and robust using realistic simulations. The dom- By excluding them,2 ! we increase± the median redshift of where the 68%CL! error" includes statistical errors, cosmic inant systematic effects associated with interferometric variance,the source and systematic sample andeffects. thus expect the lensing signalobservations to were studied in detail. The analytical and Recentincrease. cosmic Fig. shear 15 measurements shows the M inap thestatistics optical band for thissimulated new expectations of the systematics compared well with the data when considered functions of four obser- yieldsample. values ofTheσ8 E-modebetween signal 0.7 and has 1.0 a for significanceΩm 0.3 of 3.6σ,as ! vational parameters. We corrected the systematics both andmeasuredΓ 0.21 at(Bacon the θ et al.450 2003;! scale. Brown Compared et al. 2003; to Fig. 13, the ! ∼ in this parameter space and in the correlation function HamanaE-mode et al. signal 2003; on Hoekstra scales et 300 al.! ! 2002;θ ! Jarvis700! is et indeed al. larger 2002; Massey et al. 2003; Refregier, Rhodes, & Groth domain, and verified the accuracy of the corrections with by 10-20%. This confirms the presence of the lensingfurther simulations. 2002;signal Rhodes, on theseRefregier scales. & Groth 2004; van Waerbeke et al. 2002). The averaged constraint from several of these Using the corrected shear correlation functions, we As an interesting exercise, we calculate the mediancomputed red- the aperture mass statistic, which decomposes surveys is σ8 =0.83 0.04 (as compiled by Refregier ± the signal into E- and B-modes, containing the lensing 2003)shift for derived the same from values the of Ω DPm and redshiftΓ.Theconstraint, models (see 3.2) by Fig. 15.— Same as Fig. 13, but this time for only those sources § signal and the non-lensing contributions, respectively. σ8 =0excluding.9 0.1(68%CL),fromtheWMAPCMBexperi- the z<0.3region;thevariousmedianred- lacking optical counterparts in the APM catalog. mentshifts (Spergel± shown et al. in 2003) Fig. is 1 also increase shown by in Fig. about 16. 10-15%. For We Since find that the B-modes are consistent with 0 on all scales considered, while the E-modes displays a signifi- source redshifts in the range 1.4 ! zm ! 3.4, our results2 the Map lensing signal increases roughly as zm to firstcant or- lensing signal. The E-mode signal has a significance areder, consistent the changes (within in 1σ)withbothofthesedi the measured lensingfferent signal wrought measurements. Reversing the argument and taking the of 3.0σ,asmeasuredattheMap values withθ 450θ >! scale.200!,thusavoidingsub-pointing The signal by the exclusion of the low-redshift sources is consistentincreases by 10-20% when sources∼ with optical counter- WMAP determination of σ8 as a prior, we find that the scales which have unreliable systematics correction (see medianwith redshift that expected of the radio from sources the in consequentour sample (with- changeparts in the (and, therefore,discussion predominantly above). The at low covariance redshift) are matrix is computed excluded. This confirms the presence of a lensing signal outestimated APM counterpart)zm from is z them =2 models..2 0.9at68%CL.This ± which is expectedfrom to the increase field-to-field as the mean variations source redshift as described in 6.3 and redshift range is also consistent with the models for the is given by § radio source redshift7.2. distributionCosmological described Implications in 3.2. increases. § Using the E-mode Map statistics on scales 200! < θ < 8. CONCLUSIONS Σn(din di )(dj n dj ) Using the Map statistics from the sample without1000 opti-! (corresponding to physicalWij = scales from−# about$ 1◦ −# $ , (36) cal counterparts, we fit cosmological models to our data N(N 1) 2 − by computing the χ values: where the sum is over different subsamples n,andN =12 2 T 1 is the total number of subsamples. The di’s are the Map χ =(d m) W− (d m), (35) − − E-mode values at different scales, and di is their av- # $ where d is the Map data vector, m is the ΛCDM model erage over all 12 fields. Since the B-modes quantify the vector and W the covariance matrix. For d we use the contamination from systematics and are consistent with Weak lensing with the Square Kilometre Array M. L. Brown

Figure 1: Left panel: The redshift distribution of source galaxies for a 1000 deg2 weak lensing survey requiring 2 years observing time on the SKA1-early facility. Also shown is the redshift distribution for the Continuum1500 deg2 VST-KiDS optical lensing surveys survey. The n(z) extends : to gravitational higher redshifts in the radio survey and lensing probes a greater range of cosmic history. Right panel: The corresponding constraints on a 5-bin tomographic power spectrum analysis. For both experiments, we assumed an RMS dispersion in ellipticity measurements of grms = 0.3 and the tomographic bins have been chosen such that the bins are populated with equal numbers of galaxies.What Note how theis radio the survey potential extends to higher redshifts radio where the lensingadvantage? signal is stronger and therefore• easier to measure. Open triangles denote 1s upper limits on a bandpower. Note that only the auto power spectra in each bin are displayed though much cosmological information will also be encoded in the cross-correlationProbing spectra to betweenhigh theredshifts different z-bins. PSF calibration a challenge in optical

Shape estimates with uncorrelated systematics between radio/optical Mapping the dark matter with polarized radio surveys 5

Heymans, C. et al. 2008, MNRAS, 385, 1431 Hirata C. M., Seljak U., 2004, Phys. Rev. D, 70, 063526 Kaiser, N. 1998, ApJ, 498, 26 Figure 2: As Fig. 1 but for a 5000 deg2 weak lensing survey requiring 2 years observing time on the Kaiser, N. & Squires, G. 1993, ApJ, 404, 441 Estimates of intrinsic shape using Kronberg P. P., Dyer C. C., Burbidge E. M., Junkkarinen V. T., 1991, ApJ, full SKA1 facility. Also shown for comparison are the n(z) distribution and forecasted power spectrum 367, L1 2 2 constraintspolarization for the 5000 deg and/orDark Energy Survey.velocity maps Kronberg P. P., Dyer C. C., Roeser H., 1996, ApJ, 472, 115 Massey, R. et al. 2007, Nature, 445, 286 Muxlow, T. W. B. et al. 2005, MNRAS, 358, 1159 Owen, F. N. & Morrison, G. E. 2008, AJ, 136, 1889 ing photometric and spectroscopic redshift estimates for the background galaxy population. For Schrabback, T. et al. 2010, A&A, 516, A63+ Seitz, C. & Schneider, P. 1995, A&A, 297, 287 SKA1-early, we have assumed that we have no spectroscopic redshift information and that we have Stil, J. M., Krause, M., Beck, R., & Taylor, A. R. 2009, ApJ, 693, 1392 White, M. 2005, Astroparticle Physics, 23, 349 photo-z estimates from overlapping optical surveys with errors sz = 0.05(1 + z) up to a limiting Wilman, R. J. et al. 2008, MNRAS, 388, 1335 redshift of 1.5. To model the much larger uncertainties expected for the high-z radio galaxies, we adopt s = 0.3(1 + z) so that a z = 2 galaxy has a redshift uncertainty of 1. For SKA1, we z ± ⇠ additionally assume that we will have spectroscopic redshifts from overlapping HI observations for 15% of the z < 0.6 population. Finally for SKA2, we assume we have spectroscopicFigure 3. Predicted redshifts per-multipole uncertainties on the weak lensing power Morales (2006) Brown2 & Battye (2010)−2 Fig. 1.— This cartoon illustrates the effects of lensing on a velocity map. Panel a) shows a representative velocity map without lensing. spectrum for a 5000 deg survey with n¯ =15arcmin and !rms =0.3. The The axis of rotation is oriented 60◦ from the line of sight, with the grey value indicating the observed radial velocity. The image is then forecasts using the polarization estimator assume that one third of these lensed by s1 & s2 to produce the image in panel b). The orientation of the axis along the radial velocity maximum (mv )andthezero α velocity axis (m0)areatrightanglesintheunlensedimage,buthavealargerangle α in the lensed image. The observed angle α directly galaxies are detected sufficiently well in polarization suchthat rms =7degs. measures the weak lensing, as described in detail in the text.Inthelimitofashear-onlyfield,6 α directly measures the component of the The cosmic variance limit is also shown for comparison. shear indicated by s1 & s2,i.e.theshearcomponentalignedwiththebisectorofα.(Forthisexamplealargevalueofκ = γ =0.2, equivalent to an isothermal mass distribution centered directly below the lensed galaxy, was used for illustration purposes.)

The image in panel b) clearly shows the increase in An equivalent way of viewing the lensing transforma- ellipticity and tangential alignment of the lensed image tion is that the lens sees a flat projected image of the that are used in standard weak lensing measurements. galaxy with the characteristic cross-shape in the velocity Note however, that while the zero and maximum veloc- map (m0 ⊥ mv as shown in the left-hand panel). The ity axes are aligned with the major and minor axes of observer then sees that image rotated around the s2 axis the unlensed image, this is no longer true for the lensed (out of the image plane) by the lens. As the rotation image. around s2 increases, the angle α also increases. Look- To explore the properties of this distortion further, ing at the lens transformation as a rotation of the initial we note that α only depends on the convergence κ to velocity map out of the image plane naturally leads to second order, and we can safely neglect this small con- efficient algorithms for detecting the weak lensing signa- tribution for the remainder of this discussion. To first ture in the observed velocity map. order, α then only depends on the component of the 2.1. Error characteristics shear orthogonal to the initial velocity axes m0,mv,or equivalently the component of the shear aligned with the The observational applicability of measuring weak bisector of α and shown by s1,s2 in Figure 1. (Note lensing with velocity maps depends on the error charac- that shear axes are orthogonal under 45◦ rotations, see teristics inherent to the technique. The three primary er- Cabella & Kamionkowski (2005) for a nice discussion of ror characteristics of velocity map lensing measurements the mathematical properties.) shear along the orthogo- are: nal m0,mv orientation will change the ellipticity of the Reduced number counts. The most obvious change is observed image, but will not change the orientation of the the reduced number counts. Because the ellipticity noise velocity axes. To first order α measures the component has been eliminated, in principal only two galaxies are of the shear field aligned with the bisector of α. needed to measure the shear as opposed to hundreds. The orientation of the shear component measured by This advantage is offset by the much smaller flux from α is determined by the observed orientation of the lensed emission lines compared to the integrated luminosity. galaxy. To measure the total shear in a small region thus The observational implications come down to the relative necessitates determining γ for two nearby galaxies with strength of the line emission, and the galaxy luminosity different observed orientations θ1, θ2.Ifweindicatethe function, and is discussed in more depth in Section 3. true shear field as %+, %× (often chosen so %× =0),then Uncertainty depends on brightness of the image. More the component of the shear measured with each galaxy importantly, the precision of the lensing measurement is increases with the brightness of the galactic velocity im- age until limited by systematic errors. In standard weak γ = % cos 2θ + %× sin 2θ , (4) 1 + 1 1 lensing observations, bright galaxies are no more useful γ2 = %+ cos 2θ2 + %× sin 2θ2. (5) than faint galaxies due to the unknown intrinsic elliptic- These can be easily solved to find ity, and all galaxies are weighted the same. With velocity maps, the uncertainty in the shear keeps decreasing with γ2 sin(2θ1) − γ1 sin(2θ2) %+ = − . (6) the uncertainty in the image. This makes bright galaxies sin(2θ1 2θ2) much more valuable, and changes the way one tries to If the orientation of the shear is already given by a mass perform the observations (a few bright galaxies may be model, then only one galaxy is needed to obtain a mea- sufficient). surement. Reduced systematics. Systematic errors can be more Continuum surveys : gravitational lensing • What are the challenges?

Credit : http://radiogreat.jb.man.ac.uk Continuum surveys : non-Gaussianity • Largest-scale structure contains primordial imprint

Ferramacho et al. (2014)

Seljak (2009)

Radio Galaxy populationsCosmology with SKA Radio and Continuum the Surveys multi-tracer technique 3

Figure 2: Forecast constraints on fNL obtained with the multi-tracer method as a function of the flux-density Figure 1. Left: 3D halo power spectrum at z=1 for different values of fnlthresholdwith used an to e detectffective galaxies. halo The bias various (eq. populations 6) computed considered are in FR-I the and mass FR-II radio range galaxies, 11 −1 12 −1 13 −1 14 −1 3D from 10 h M" to 10 h M"(lower curves) and from 10 h M" radio-quietto 10 quasars,h M star-forming" (Upper galaxies curves). and starburstRight: galaxies,Ratio with different between biases, as the describedPh in both Wilman et al. (2008) and Ferramacho et al. (2014). We present the results obtained using the full sample of curves presented on the left panel for the same values of fnl. objects with an averaged effective bias and those obtained using the combination of 3 populations of radio galaxies (where SRG, SB and RQQ correspond to one population group), using 4 populations (where only SFG and SB are undifferentiated) and with a selection of 5 populations for z < 1 and 4 populations for z > 1 tics. More massive halos will then be more sensitive to non- ple(again are with undifferentiated the Luminous SFG and SB). Red We also Galaxies show the result (LRGs), for the ideal case a wherepopulation all 5 populations could be differentiated over the entire redshift range of the survey. The horizontal line represents the best Gaussianity than lower mass ones. Fig. 1 shows this effect for ofconstraint old andobtained relaxed by the Planck galaxies collaboration (Planckexpected Collaboration to be et al. free2013c). from Taken from recent Ferramacho et al. (2014). different values of fnl and halo mass for the 3D halo power merger activity. Such properties justify the use of these ob- spectrum. One can clearly see the differential effect of using jects to reconstruct the halo density field (Reid et al. 2010) us to study scales at z 1 that have not been in causal contact since the first horizon crossing during mass bins, with the effect being significant only for k less and use the resulting⇠ power spectrum to constrain cosmolog- −1 inflation, and therefore contain information that was frozen in during cosmological inflation. than 0.02 hMpc ,andhavingarelativeamplitudeupto icalSKA models all-sky surveys (Percival will allow et the al. measurement 2010) of including the cosmic radio the dipole presence almost as precisely of order 1 order of magnitude. Such features offers the possibil- non-Gaussianityas the CMB dipole. SKA1 (Bernardis will constrain the et cosmic al. radio2010). dipole However, direction with even an accuracy with better than 5 degrees (Fig. 3), and SKA2 within a degree (at 99 per cent C.L.). Compared to todays best ity to obtain additional information on fnl by constructing this analysis, it is not possible to differentiate the mass of estimate based on NVSS data, this will be an improvement of a factor of 100 in the accuracy of observational 2-point statistics from objects corresponding thethe cosmic halos radio associated dipole direction with for SKA1. LRGs This measurementand constraining could firmly establishfnl is or done refute the to different halo mass ranges. In order to exploit this, we bycommonly means adopted of assumptionan effective that thebias, CMB and corresponding the overall large-scale to structure a weighted frames agree. need to address the issue of differentiating halo masses from averagedThe CMB bias exhibits over unexpected the mass features range at the largest expected angular scales,for halos among hosting them a lack of an observational point of view. agivengalaxytype(e.g.LRGs):angular correlation, alignments between the dipole, quadrupole and octopole, hemispherical asym- metry, a dipolar power modulation, and parity asymmetries (Planck Collaboration et al. 2013b; dn bh(M,z) dzdM dM bef f (z)= , (6) 6 dn dM 3GALAXYBIAS ! dzdM where dn/(dzdM)isthehalomassfunction.Theabove! 3.1 Tracers of halo mass equation has been used to place constraints on non-Gaussian Most of the studies done to constrain clustering properties of bias using 3D power spectrum from large available datasets dark matter are based on large surveys of galaxies or clusters and thus reducing the shot noise component at the expense that trace the distribution of matter over large scales in the of some loss of information on fnl. Universe. A key issue when modeling the data obtained from LSS surveys is to know how galaxies populate dark matter 3.2 Radio galaxy populations halos. This is a complex issue since galaxy formation involves non-linear collapse inside the collapsed halos and there is Adifferent approach is to consider other specific galaxy pop- also the possibility of merging form different sized halos. ulations whose bias properties can be explained by a strong One way to address this issue is to adopt the Halo model correlation between halo mass and galaxy type. This seems (Cooray & Seth 2002) which assumes an Halo occupation to be the case for some types of radio galaxies, such as Radio- Distribution function (HoD) to compute the galaxy power quiet and Radio-loud AGNs, including FRI and FRII galax- spectrum. In this framework, all the information about the ies (Fanaroff & Riley 1974), and also star-forming galaxies, mass dependent features is compressed into a few free pa- including starbursts. The idea of assigning a single halo mass rameters such as the minimum mass of haloes that can con- to these objects was introduced by Wilman et al. (2008) tain galaxies as observed in a survey. The Halo model is (W08) in a framework to produce realistic sets of data of averyusefultooltoaccuratelycomputethegalaxypower the extragalactic sky to be observed with the next genera- spectrum into the non-linear scales, but by incorporating all tion of radio telescopes. Indeed, for low redshifts the (scale types of galaxies in the HoD the information on halo mass independent) bias obtained using the formalism presented at large scales is not taken into account. in section 2.2 with a single halo mass for each population is Another way to access the halo clustering properties compatible with the clustering measurements obtained from is to consider specific populations of galaxies and clusters the NVSS (Condon et al. 1998) and FIRST (Becker et al. which allow the elimination of the one-halo contribution to 1995) surveys (e.g. Blake & Wall 2002; Overzier et al. 2003; the power spectrum, and thus more directly trace each ob- Blake et al. 2004; Wilman et al. 2003; Lindsay et al. 2014). ject with its underlying dark matter halo. A typical exam- The mass to be assigned to each galaxy type is thoroughly

!c 0000 RAS, MNRAS 000,000–000 TheContinuum dark energy surveys puzzle : homogeneity and isotropy • Are CMB “anomalies” cosmologically interesting?

Foundations of modern cosmology Dominik J. Schwarz

precission of radio dipole direction; efficiency 50% Test with radio CMB: z ~ 1100 30

galaxy dipole degrees 25 in

CL 20 SKA radio sky % 99 d radio 15 us

d CMB and Blake & Wall (2002) z < 1

CL 10 > z 1 % 95

, 5

Rubart & Schwarz (2013) CL % 0 90 104 105 106 107 108 109 1010 number of observed radio point sources

Figure 1: Left: All-sky (3p) SKA surveys (yellow and orange) will measure the cosmic radio dipole of differential source counts. Selecting AGNs will result in a sample with median redshift z > 1 (orange) and thus allow us to measure the peculiar velocity of the solar system with respect to the large scale structure on superhorizon scales. These measurements will be compared to the CMB dipole and thus test for the existence of a bulk flow of our Hubble volume compared to the CMB rest frame. Right: Angular accuracy at 90, 95 and 99 % C.L. of the measurement of the cosmic radio dipole as a function of observed point sources. The blue set of curves assumes dradio = 4dcmb, the red set assumes dradio = dcmb. It is assumed that only 50% of all detected radio sources survive all quality cuts (e.g. masking fields that contain very bright sources). Combined with Table 1 we find that SKA Early Science allows detection of a possible deviation from the CMB expectation at high significance. SKA1 will constrain the cosmic radio dipole direction with an accuracy better than 5 degrees, SKA2 within a degree (at 99% C.L.).

120 60 isotropic, x=1 isotropic, x=1 cosinus, x=1 cosinus, x=1 100 cosinus, x=1.5 40 cosinus, x=1.5 cosinus, x=0.5 cosinus, x=0.5 80 Shot noise 20 Shot noise error 60 0 θ in percent

error 40 -20 absolute 20 -40 relative d 0 -60

-20 -80 0.01 0.1 0.01 0.1 sigma sigma

Figure 2: Left: Accuracy (in per cent) of the measurement of the dipole amplitude as function of fractional error on flux density calibration on individual point sources. All points are based on 100 simulations. Right: Accuracy (in degrees) of the measurement of the dipole direction. The horizontal lines denote the error due to shot noise for a dipole estimate based on 107 sources (SKA Early Science).

the latitude of the SKA site and d d < 70 deg. For two cases we find negligible influence of | ⇤| calibration errors: If the flux calibration error is completely isotropic or if the slope x of the number x counts [N(> S) µ S ] is equal to one. It turns out that x = 1 is a special value, where calibration errors at the lower flux density limit have no influence on the dipole estimator. We conclude that direction dependent calibration effects must not exceed certain limits as shown figure 2. Another significant contaminant of the kinetic radio dipole is the local structure dipole. We can turn a disadvantage of continuum surveys, namely that we observe several source populations, into an advantage as follows: The lower mean redshift of SFGs compared to AGNs allows us to change

5 Cosmology with the SKA

• Use HI intensity mapping to measure large-scale structure across large volumes to high redshift

• Test cosmology with cross-correlations of the radio continuum survey with CMB and optical surveys

• Measure weak gravitational lensing in radio continuum observations using new techniques

• Constrain primordial non-Gaussianity using the largest-scale modes