2. Goals and methods Goals: testing Lambda CDM model and its extensions Testing inflation Methods: redshift distance relation (SN, BAO…) Linear perturbations: RSD, WL… Consistency, complimentarity, future data sets… 2

3. Neoclassical tests We wish to test Friedmann equation: redshift-distance Redshift-distance relation has come a long way since the days of Hubble (and people before him) 3 But we are celebrating CMB, so…

4. Baryonic Acoustic Oscillations Each initial overdensity (in DM & gas) is an overpressure that launches a spherical sound wave. This wave travels outwards at 57% of the speed of light. Pressure-providing photons decouple at recombination. CMB travels to us from these spheres. Sound speed plummets. Wave stalls at a radius of 147 Mpc. Seen in CMB as acoustic peaks Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 147 Mpc. 4

5. A Standard Ruler The acoustic oscillation scale depends on the matter-to-radiation ratio (  m h 2 ) and the baryon-to-photon ratio (  b h 2 ) The CMB anisotropies measure these and fix the oscillation scale to <1%. In a redshift survey, we can measure this along and across the line of sight: BAO along los BAO tranverse Yields H(z) and D M (z)

6. BOSS/SDSS-III survey 6 10,000 square degrees 1.5M galaxy redshifts 160k QSO Lya forest

7. Hunting for BAO: correlation function and power spectrum 7

8. BAO reconstruction BAO is damped due to nonlinear evolution Easiest to see in Zeldovich approximation, for which we have an analytic expression for P(k): BAO is damped by P w /P nw =exp(-k 2  2 /2), where  is rms displacement between two particles separated by 147Mpc Reconstruction: take final density and estimate a filtered displacement field, move particles back with displacements, take random (uniform) particles and displace them, add the two Reconstruction reduces  for both fields (Padmanabhan, White, Cohn) At 2nd order in PT removes BAO shifts Reconstruction does not reconstruct linear density 8 Eisenstein, Padmanabhan, White…

9. 9 Simulations: reconstruction removes BAO shifts, but those are tiny One can achieve almost the same S/N by adding bispectrum Schmittful etal

10. SDSSIII/BOSS Lya survey 10

11. BAO Hubble diagram 11 Aubourg etal (BOSS coll)

12. Inverse distance ladder SN1A are standard candles, but to get H 0 need absolute calibration Standard ladder: stellar calibration (cepheids to SN host galaxies…) Inverse ladder: BAO is a standard ruler with a known absolute calibration, and at z=0.57 overlaps with SN1A, allowing absolute calibration of SN1A, bringing it down to z=0 gives H 0 12

13. Comparison of H 0 Perfect agreement with Planck CMB Some discrepancy with direct distance ladder 13

14. What about Lya discrepancy? 14 Delubac etal 2014 Font-Ribera etal 2014 Aubourg etal 2014 2.5 sigma discrepant with Planck No reasonable model can explain it (need “crazy” models like tuned oscillations)

15. What to expect from BOSS DR12 Volume increase by 15% Lya BAO updates: many systematics checks, no issues found so far Small increase in errors+small shifts: current discrepancy with Lambda CDM less than 2 sigma CMASS/LOWZ BAO updates: “optimal analyis” under way, not expected to yield major changes vs DR11 Huge improvements expected in RSD/AP due to better nonlinear modeling SDSS-IV (eBOSS) is already underway 15

16. Growth of structure by gravity  Perturbations can be measured at different epochs: 1. CMB z=1000 2. Ly-alpha forest z=2-4 3. Weak lensing z=0.3-2 4. Galaxy clustering, clusters z=0-2 Sensitive to matter components, initial conditions…

17. Shape of matter power spectrum 17 Picture from Binney & Tremaine Nearly scale- invariant spectrum Suppression on small scales Probes initial conditions We measure redshifts and angles, and the shape is not a power law, so there are neoclassical tests in broadband measurements as well

18. Measures 3-d distribution, has many more modes than projected quantities like shear from weak lensing Easy to measure: effects of order unity, not 1% SDSS Galaxy clustering in redshift space

19. Galaxy power spectrum: biasing Galaxy clustering traces dark matter clustering Amplitude depends on galaxy type: galaxy bias b To determine bias we need additional information Galaxy bias can be scale dependent: b(k) Once we know bias we know how dark matter clustering grows in time Tegmark et al. (2006) P gg (k)=b 2 (k)P mm (k)

20. How to determine bias? Redshift space distortions redshift cz=aHr+v p 20

21. RSD in linear regime 21 Kaiser 1984 Conservation of galaxies Jacobian drop v/z Go to Fourier space, assume v is irrotational Define  =ikv Use continuity equation

22. Linear and nonlinear effects 22 White etal 2011 On very large scales linear RSD distortions: Kaiser formula From angular dependence we can determine velocity power proportional to f   On small scales: virialized velocities within halos lead to FoG, extending radially 10 times farther than transverse

23. Nonlinear RSD effects are huge 23 Simulations vs model Vlah, US etal 2013 Nonlinear gravity Nonlinear bias Nonlinear velocities (FoG) In correlation function one can get quite far with Zeldovich approximation In P(k) standard perturbation theory+bias

24. RSD observations state of the art: SDSS-III/BOSS DR11 24 f    z   Reid et al 2012, Samushia et al 2013, Beutler et al 2013 

25. SDSS DR11 25 Beutler etal 2014 Current models go to k=0.1-0.2h/Mpc, monopole and quadrupole only There is a lot more information at high k

26. Can we model quasi-linear regime and extract more information? Need to develop nonlinear models that are sufficiently general to allow for any reasonable nonlinear effects present in the data, while preserving as much of cosmological information as possible Some can be modeled by perturbation theory (PT) There is always more information on small scales, but most of it is hopelessly corrupted by nonlinear effects that cannot be modeled in PT One needs to model our ignorance that is genteel (no sharp k or r cutoffs) and obeys all symmetries (e.g. k 2 P L (k) at low k) and all physics (the parameters are physical, e.g. FoG is determined by halo mass…) In recent years a workhorse has been the halo model+PT 26

27. Halo model Use PT (e.g. Zeldovich, SPT…) to describe large scales Use halo picture to describe small scales Halo description: halo profile: take moments Expand in (even) powers of k P 1halo =A 0 k 0 -A 2 k 2 +A 4 k 4 +… P 2halo =P L (k)(1-A 2 k 2 …) (or replace P L with PT version) FoG: cannot use low k expansion, need to resum the terms P 1halo =A 0 G(k), P 2halo =P L (k)G(k) 27

28. Modeling FoG 28 Lorentzian does a reasonable job Low k expansion G(k)=1-k      v /2 1% valid only to k=0.1h/Mpc (this is EFT domain) Value of   v determined by the halo mass (strong prior) Okumura etal 2015

29. Example: modeling of CMASS in simulations 29 Okumura etal 2015 Linear Kaiser never a good model NL model achieves 1% to k=0.4h/Mpc by introducing many physical parameters in the PT model: central and satellite galaxies, each with a bias and FoG, 1-halo contribution from central-satellite pairs, halo exclusion… A lot of neoclassical test information in here (AP parameter D M /D H )

30. A reward for the hard work 2.5% determination of f  8 in DR11 (more than 2x reduction of error) by using information from very small scales Needs to be tested more, marginalized… 30 Reid etal 2014

31. Weak Gravitational Lensing: sensitive to total mass distribution (DM dominated) Distortion of background images by foreground matter UnlensedLensed

32. Convergence and shear convergence Convergence shear relation in Fourier space shear

33. Method A: shear-shear correlations Just a projection of total matter P(k) Need P(k) for dark+baryonic matter: a lot of information in nonlinear regime Dark matter is easy Sensitive to many cosmological parameters

34. State of the art in shear-shear: CFHT-LS 34 Challenges: Small scales: could be contaminated by baryonic effects Redshift distributions not completely known Various systematics: a lot of data removed DES/HSC data coming soon! Kiblinger et al 2013

35. Effect of gravitational lensing on CMB Here  is the convergence and is a projection of the matter density perturbation. Lensing creates magnification and shear Okamoto and Hu 2002

36. State of the art in CMB lensing: Planck 36 40 sigma in Planck 2015

37. What about baryonic (astrophysical) effects? astrophysical effects that redistribute matter inside the halos change mass distribution (AGNs…), but not total mass Parametrizing ignorance with the halo model: change 1 halo term A 2, A 4 …, but not A 0, there is also a small 2 halo term With proper modeling and marginalization these effects do not reduce information substantially 37

38. WL Method B: galaxy-shear correlations Cross-correlation proportional to bias b Galaxy auto-correlation proportional to b 2

39. Simulations: dark matter reconstruction Cross-correlation coefficient r nearly unity Baldauf, Smith, US, Mandelbaum (2009) Nonlinear linear

40. SDSS DR-7 data analysis Mandelbaum etal, 2013 LENSES SOURCES 70,000 M*-1 galaxies (z<0.15), 10M, well calibrated photozs 62,000 low z LRGs (0.16<z<0.3),using spectroscopic surveys 35,000 high z LRGs (0.36<z<0.47)

41. Complementarity of RSD vs WL Science complementarity: f vs  m, tests of modified gravity… 41

42. WL and RSD: reasons for optimism WL: theoretical uncertainties (almost) under control WL+RSD: many redundancy tests can be done: higher order correlations, scale dependence of the signal… RSD and WL B: many different ways to slice the data (e.g. remove close pairs, split by luminosity or color…), and to analyze the data (e.g. remove line of sight pairs) in the end they all have to agree to believe the results Cluster abundance methods will be covered by others: measure one number, redundancy checks? 42

43. Lya 1d P(k) 43 Some tension with Planck, issues related to IGM simulations limit the accuracy

44. Neutrino mass can be measured by LSS Neutrino free streaming inhibits growth of structure on scales smaller than free streaming distance If neutrinos have mass they contribute to the total matter density, but since they are not clumped on small scales dark matter growth is suppressed Minimum signal at 0.06eV level makes 4% suppression in power, mostly at k<0.1h/Mpc SDSS coud reach this at 1sigma, DESI at 2-3 sigma LSS: weak lensing of galaxies and CMB, galaxy clustering m=0.15x3, 0.3x3, 0.6x3, 0.9x1 eV

45. Combining LSS probes 45 To break this degeneracy we need BAO+CMB:  m =0.31+/-0.02 Probes: CFHTLS WL, BOSS RSD, SDSS-III WL, cluster abundance, tSZ At the moment LSS, even if combining all data sets, has a larger error on amplitude than Planck CMB lensing But LSS+Planck is more sensitive to neutrino mass

46. Planck vs LSS 46 Reasonable consensus between Planck+BAO and LSS zero neutrino mass becoming disfavored at 2- sigma, cannot distinguish between normal and inverted hierarchy

47. Planck+LSS 47 A powerful combination: CMB+BAO+LSS (lensing…) adding Planck lensing and BAO to Planck reduces error on curvature by 12!

48. Future imaging surveys: DES, HSC, Euclid, LSST, Wfirst, (Spherex?)… Plan: 10 8 -10 9 galaxies (without redshifts) Future spectroscopic surveys: DESI, PFS, Euclid, Wfirst… Plan: 10 7 galaxies (with redshifts) Future CMB lensing (S3, S4) New technique: 21cm, both for BAO (Chime…) and reionization (Hera, SKA…) Future data

49. Predictions for future data sets: Planck+DESI+LSST+S4+… Curvature  k to 0.07%: could be improved with CMB lensing, but still a long way from cosmic variance limit n s, dn s /dlnk to 0.0015 with Lya forest P 1d, otherwise 0.005, Spherex can also reach 0.001: test inflation? f nl to 1, possibly to 0.2 with Spherex M  to 0.02eV, limited by Planck optical depth uncertainty: can we do better (21cm?) 49 Font-Ribera etal 2014…

50. Modeling challenges in LSS surveys Better modeling of the ignorance Higher order correlations (including primordial nongaussianities etc.) Other types of analysis (peaks, voids…) Covariance matrix modeling with and without simulations No mode left behind: extract all the linear modes up to the noise using forward or backward modeling 50

51. Summary BAO+SN+CMB: a winning combination of neoclassical tests LSS: RSD and WL have a lot of promise, lots of redundancy, best results come from CMB lensing Amplitude of fluctuations at z<1 determined by several probes: 3- 10% precision (CMB WL, RSD, clusters, tSZ C l ) Some are high, some are low, some consensus at  8 =0.78-0.80. Is this lower than Planck lensing? No evidence of neutrino mass yet:  m  0.20eV (95%), but likelihood not peaking at m  anymore (at 1-2sigma) No evidence of curvature, despite 1 order of magnitude improvement in last year Future LSS probes will do a lot better 51