1. Overview of Large Scale Structure Uros Seljak Zurich/ICTP/Princeton/Berkeley/LBL Hamilton, may 16, 2007

2. Outline 1)Methods to investigate dark energy and dark matter: galaxy clustering, cluster counts, weak lensing, Lya forest 2)Issues of systematics and statistics 3)Current constraints: what have we learned so far, controversies 4) What can we expect in the future?

3. How to test dark energy? 1)Classical tests: redshift-distance relation (SN1A etc)… 2)Growth of structure: CMB, Ly-alpha, weak lensing, clusters, galaxy clustering 3)Scale dependence of structure (same tracers as above)

4. Growth of structure by gravity  Perturbations can be measured at different epochs: 1. CMB z=1000 2. 21cm z=10-20 (?) 3. Ly-alpha forest z=2-4 4. Weak lensing z=0.3-2 5. Galaxy clustering z=0-2 Sensitive to dark energy, neutrinos…

5. CBIACBAR Lyman alpha forest Scale dependence of cosmological probes WMAP Complementary in scale and redshift SDSS Galaxy clustering Weak lensing Cluster abundance

6. Sound Waves from the Early Universe Before recombination: –Universe is ionized. –Photons provide enormous pressure and restoring force. –Perturbations oscillate as acoustic waves. After recombination: –Universe is neutral. –Photons can travel freely past the baryons. –Phase of oscillation at t rec affects late-time amplitude.

7. This is how the Wilkinson Microwave Anisotropy Probe (WMAP) sees the CMB

8. Determining Basic Parameters Angular Diameter Distance w = -1.8,..,-0.2 When combined with measurement of matter density constrains data to a line in  m -w space (in the absence of curvature)

9. Determining Basic Parameters Matter Density  m h 2 = 0.16,..,0.33

10. Determining Basic Parameters Baryon Density  b h 2 = 0.015,0.017..0.031

11. Current 3 year WMAP analysis/data situation Current data favor the simplest scale invariant model

12. Galaxy and quasar survey 400,000 galaxies with redshifts Galaxy surveys: SDSS and 2dF

13. Shape and acoustic Oscillations in the Matter Power Spectrum Shape determined by matter and baryon density Amplitude not useful (bias) Peaks are weak; suppressed by a factor of the baryon fraction. Higher harmonics suffer from diffusion damping. Requires large surveys to detect! Linear regime matter power spectrum

14. Galaxy power spectrum: shape analysis Galaxy clustering traces dark matter on large scales Current results: redshift space power spectrum analysis based on 200,000 galaxies (Tegmark etal, Pope etal), comparable to 2dF (Cole etal) Padmanabhan etal: LRG power spectrum analysis, 10 times larger volume, 2 million galaxies Amplitude not useful (bias unknown) Nonlinear scales

15. Power Spectrum LRG analysis in Fourier space with a quadratic estimator for the power spectrum. See also FKP analysis in Percival et al. (2006). Tegmark et al. (2006)

16. Systematics: nonlinear bias Need to model nonlinear bias Current analyses use Q model (Cole etal), where Q is either fixed from simulations (Q=5-10 for normal galaxies, Q=20-30 for LRGs in real space) or determined from the data by going to smaller scales (k=0.3h/Mpc) Do NOT allow for Q to be free and only use k<0.1h/Mpc data (eg in Hamann etal 2007 they find even Q=60-100 is acceptable, completely incompatible with the data at k=0.2-0.3h/Mpc) Need to move to a better model, but it is uncertain how much we will gain for cosmology

17. Are galaxy surveys consistent with each other? Some claims that SDSS main sample gives more than 2 sigma larger value of  Need to account for nonlinear bias SDSS LRG photo 2dF SDSS main spectro Bottom line: no evidence for discrepancy if one marginalizes over nonlinear bias, new analyses improve upon SDSS main Fixing h=0.7 Padmanabhan etal 2006

18. Sound Waves 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 150 Mpc. Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc.

19. 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. In a redshift survey, we can measure this along and across the line of sight. Yields H(z) and D A (z)! Observer  r = (c/H)  z  r = D A 

20. Sloan Digital Sky Survey (SDSS) Image Credit: Sloan Digital Sky Survey 2.5 m aperture 5 colors ugriz 6 CCDs per color, 2048x2048, 0.396”/pixel Integration time ~ 50 sec per color Typical seeing ~ 1.5” Limiting mag r~23 current 7000 deg 2 of imaging data, 40 million galaxies 400,000 spectra (r<17.77 main sample, 19.1 QSO,LRG)

21. Baryonic wiggles Best evidence: SDSS LRG spectroscopic sample (Eisenstein etal 2005), about 3.5 sigma evidence SDSS LRG photometric sample (Padmanabhan, Schlegel, US etal 2005): 2.5 sigma evidence 2dF comparable evidence

22. Current BAO constraints SDSS LRG correlation function does show a plausible acoustic peak. Ratio of D(z=0.35) to D(z=1000) measured to 4%. –This measurement is insensitive to variations in spectral tilt and small-scale modeling. We are measuring the same physical feature at low and high redshift.  m h 2 from SDSS LRG and from CMB agree. Roughly 10% precision. –This will improve rapidly from better CMB data and from better modeling of LRG sample.  m = 0.273 ± 0.025 + 0.123(1+w 0 ) + 0.137  K.

23. Concept proposed for the Joint Dark Energy Mission (JDEM). 3/4-sky survey of 1<z<2 from a small space telescope, using slitless IR spectroscopy of the H  line. SNe Ia to z~1.4. 100 million redshifts; 20 times more effective volume than previous ground-based surveys. Designed for maximum synergy with ground-based dark energy programs. Fisherology predicts 0.2% error on D_a over 1<z<2 But do nonlinear effects spoil this? Smith etal 2007 argue for 1-2% random noise on peak position! TBD SYSTEMATICS are key!

24. Weak Gravitational Lensing Distortion of background images by foreground matter UnlensedLensed

25. Weak Lensing: Large-scale shear Convergence Power Spectrum 1000 sq. deg. to R ~ 27 Huterer

26. Gravitational Lensing –Advantage: directly measures mass –Disadvantages Technically more difficult Only measures projected mass- distribution Intrinsic alignments? Tereno et al. 2004 Refregier et al. 2002

27. Weak lensing: systematic errors PSF induced errors: rounding (need to calibrate), ellipticity (use stars) Shear selection bias: rounder objects can be preferentially selected Noise induced bias: conversion from intensity to shear nonlinear STEP2 project bottom line: current accuracy in best codes at 2-3% level, plenty of work to do to reach 1% level, not clear 0.1% even possible PHOTOz errors: without spectroscopy easily a 10-20% error (biasing sigma_8 high?), need complete spectroscopic surveys to the same depth! Currently this is only available for SDSS (DEEP2 and zCOSMOS data) Intrinsic alignment has been detected and one MUST deal with it! Biasing sigma_8 low by 1-10% (Hirata etal)

28. Shear-intrinsic (GI) correlation Same field shearing is also tidally distorting, opposite sign What was is now, possibly an order of magnitude increase Cross-correlations between redshift bins does not eliminate it B-mode test useless (parity conservation) Vanishes in quadratic models Hirata and US 2004 Lensing shear Tidal stretch

29. Intrinsic correlations in SDSS 300,000 spectroscopic galaxies, 36,000 LRGs No evidence for II correlations Clear evidence for GI correlations on all scales up to 60Mpc/h LRGs show the strongest signal Gg lensing not sensitive to GI Mandelbaum, Hirata, Ishak, US 2005 Hirata etal 2006

30. Up to 30% effect on power spectrum for shallow survey at z=0.5 2-20% effect for deep survey at z=1: current surveys underestimate   More important for cross-redshift bins: separate redshift bins do not eliminate Implications for existing and future surveys

31. Galaxy clustering: power spectrum shape Galaxy clustering traces dark matter on large scales Current results: redshift space power spectrum analysis based on 200,000 galaxies (Tegmark etal, Pope etal, 2dF (Cole etal) Padmanabhan etal: LRG photometric power spectrum analysis, 10 times larger volume, 2 million galaxies LRG spectro analysis: Tegmark etal, Eisenstein etal, Percival etal Amplitude not useful (bias) Nonlinear scales

32. Galaxy bias determination Galaxies are biased tracers of dark matter; the bias is believed to be scale independent on large scales (k<0.1-0.2/Mpc) If we can determine the bias we can use galaxy power spectrum to determine amplitude of dark matter spectrum  8 High accuracy determination of  8 is important for dark energy constraints Weak lensing is the most direct method

33. Galaxy-dark matter correlations: galaxy-galaxy lensing dark matter around galaxies induces tangential distortion of background galaxies: extremely small, 0.1%  Specially useful if one has redshifts of foreground galaxies: SDSS  +: Express signal in terms of projected surface density and transverse separation r: one projection less than shear-shear correlations  +: with photozs not sensitive to intrinsic alignments  -: for LSS one needs to model cross- correlation coefficient between dark matter and galaxies: simulations

34. Galaxy-galaxy lensing measures galaxy-dark matter correlations Goal: lensing determines halo masses (in fact, full mass distribution, since galaxy of a given L can be in halos of different mass) Halo mass increases with galaxy luminosity SDSS gg: 300,000 foreground galaxies, 20 million background, S/N=30, the strongest weak lensing signal to date testing ground for future surveys such as LSST,SNAP Seljak etal 2004

35. Preliminary, not yet properly calibrated Statistical error around 5% final systematic error is likely to be smaller than for other weak lensing analyses Alternative method to determine growth rate with different systematics than shear- shear correlations! Mandelbaum, US etal, in prep 2007 previous attempts: Hoekstra etal, Sheldon etal

36. WMAP-LSS cross-correlation: ISW Detection of a signal indicates time changing gravitational potential: evidence of dark energy if the universe IS flat. Many existing analyses (Boughn and Crittenden, Nolta etal, Afshordi etal, Scranton etal, Padmanabhan etal) Results controversial, often non-reproducible and evidence is weak One of the few ways to probe dark energy clustering Future detections could be up to 6(10?) sigma, not clear if this probe can play any role in cosmological parameter determination

37. WMAP-SDSS cross-correlation: ISW N. Padmanabhan, C. Hirata, US etal 2005 4000 degree overlap Unlike previous analyses we combine with auto-correlation bias determination (well known redshifts)

38. 2.5 sigma detection Consistent with other probes

39. Counting Clusters of Galaxies Sunyaev Zel’dovich effect X-ray emission from cluster gas Optical data: red sequence richness Weak lensing (future?) Simulations: growth factor

40. Galaxy Cluster Abundance Dependence on cosmological parameters growth function power spectrum (  8, M-r) Jenkins et al. 2001 comoving volume mass limit mass function # of clusters per unit area and z: mass function: overall normalization Hubble volume N-body simulations in three cosmologies cf: Press-Schechter Sunyaev Zel’dovich effect X-ray emission from cluster gas Optical data: red sequence richness Weak lensing (future?)

41. Pros and cons of cluster abundance Abundance very sensitive to cosmological parameters, specially sigma8 Many different techniques to measure clusters Need to calibrate observable to halo mass: simulations not yet reliable (resolution issues, turbulence, cosmic rays, magnetic fields…) X-ray calibration not entirely reliable because clusters are not relaxed and may hve additional pressure support (cosmic rays, bulk motions) Weak lensing reliable on average, but scatter is an issue: Malmquist and Eddington bias one can show that Malmquist bias dominates, only a robust lower limit on sigma8 can be established (Mandelbaum and US 2007) Studies that ignore scatter underestimate sigma8 Self-calibration: promising, but not for general M(L) relation

42. Cluster abundance and masses with SDSS maxBCG and LRG cluster catalogs (20-30k cluster sample!) It may be possible to give a lower limit from cluster clustering

43. Cosmic complementarity: Supernovae, CMB, and Clusters

44. Ly-alpha forest as a tracer of dark matter and dark energy Basic model: neutral hydrogen (HI) is determined by ionization balance between recombination of e and p and HI ionization from UV photons (in denser regions collisional ionization also plays a role), this gives Recombination coefficient depends on gas temperature Neutral hydrogen traces overall gas distribution, which traces dark matter on large scales, with additional pressure effects on small scales (parametrized with filtering scale k F ) Fully specified within the model, no bias issues

45. Warm Dark Matter constraints Seljak, Makarov, McDonald, & Trac, astro- ph/0602430 Flux power spectrum 3000+ SDSS spectra HIRES data probes smaller scales  2 (k) = π -1 k P(k) 0.01 s/km ~ 1 h/Mpc Colors correspond to redshift bins centered at z = 2.2, 2.4, …, 4.2 (from bottom to top)

46. SDSS Lya power spectrum analysis McDonald, US etal 2006 Combined statistical power is better than 1% in amplitude, comparable to WMAP 2<z<4 in 11 bins  2 ≈ 185.6 for 161 d.o.f.for SDSS A single CDM model fits the data over a wide range of redshift and scale WDM does not fit Ly-alpha helps by reducing degeneracies between dark energy and other parameters that Lya determines well (amplitude, slope…) Direct search for dark energy at 2<z<4 reveals no evidence for it

47. WMAP vs. LyaF (vanilla 6 parameters) Linear amp. & slope constraints at z=3, k=0.009 s/km Green: LyaF Red: WMAP Black: WMAP, SDSS-main, SN Yellow: All Blue: Viel et al. (2004) independent LyaF

48. The amplitude controversy? Some probes, Ly-alpha, weak lensing, SZ clusters prefer higher amplitude (sigma_8>0.85) Other probes, WMAP, X-ray cluster abundance, group abundance… prefer lower amplitude (sigma_8<0.80) Statistical significance of discrepancy is 2.5?- sigma or less Most likely a combination of statistical fluctuations and residual systematic effects not modeled in one or more probes In Ly-alpha most studies find that astrophysics effects (winds, UV background fluctuations, reionization…) on cosmological parameters are small, but more careful studies are needed

49. Partial degeneracy between UV background flux and amplitude is broken, factor of 3 improvement in amplitude Can determine power law slope of the growth factor to 0.1 Mandelbaum etal 2003 Upcoming analysis on SDSS Slosar etal Will provide a much better amplitude and hopefully resolve the amplitude controversy Future of LYA: more data, nongaussian signal, 3-d analysis, better modeling and simulations… Bispectrum: measuring dark energy at z>2 Simulations, not yet real data

50. Putting it all together US etal 04, 06  Dark matter fluctuations on 0.1-10Mpc scale: amplitude, slope, running of the slope  Growth of fluctuations between 2<z<4 from Lya  Lya very powerful when combined with CMB or galaxy clustering for inflation (slope, running of the slope), dark energy through growth rate comparison to z 2  still important because it is breaking degeneracies with other parameters and because it is determining amplitude at z=3.

51. Comprehensive cosmological parameter analysis: US, Slosar, & McDonald 2006 CMB: WMAP3, Boomerang-2k2, CBI, VSA, ACBAR Galaxies: SDSS-main, SDSS-LRG (BAO), 2dF SN: SNLS, Riess et al. LyaF: SDSS, HIRES

52. Dark energy constraints: complementarity of tracers US, Slosar, McDonald 2006

53. DE constraints: degeneracies and dimension of parameter space

54. Time evolution of equation of state w Individual parameters very degenerate

55. Time evolution of equation of state w remarkably close to -1 Best constraints at pivot z=0.2-0.3, robust against adding more terms In a 3 parameter expansion error at pivot remains the same as for constant w

56. To perturb or not to perturb dark energy Should one include perturbations in dark energy? For w=-1 no perturbations, otherwise ignoring them not self- consistent (no gauge invariant way to ignore them), but close to w=-1 a small effect if w is constant For w>-1 perturbations in a single scalar field model with canonical kinetic energy, speed of sound c Non-canonical fields may give speed of sound <<c For w<-1 (phantom model) one can formally adopt the same, but the model has instabilities For w crossing from -1 it has been argued that the perturbations diverge: however, no self-consistent model based on Lagrangian exists There is a self-consistent ghost condensate model that gives w<-1 (Creminelli etal 2006), perturbations in DE sector remain to be worked out

57. What if GR is wrong? Friedman equation (measured through distance) and growth rate equation are probing different parts of the theory For any distance measurement, there exists a w(z) that will fit it. However, the theory can not fit growth rate of structure Upcoming measurements can distinguish Dvali et al. DGP from GR (Ishak, Spergel, Upadye 2005) (But DGP is already ruled out)

58. A look at (almost dark) neutrinos Neutrino mass is of great importance in particle physics (are masses degenerate? Is mass hierarchy inverted?): large next generation experiments proposed (KATRIN…) Neutrino free streaming inhibits growth of structure on scales smaller than free streaming distance If neutrinos have mass they are dynamically important and suppress dark matter as well, 50% suppression for 1eV mass For m=0.1-1eV free-streaming scale is >10Mpc Neutrinos are quasi-relativistic at z=1000: CMB is also important, opposite sign m=0.15x3, 0.3x3, 0.6x3, 0.9x1 eV

63. New limits on neutrino mass WMAP3+SDSS Lya+SDSS+2dF+SN 6p: Together with SK and solar limits: Lifting the degeneracy of neutrino mass

65. Neutrino as dark matter Initial conditions set by inflation (or something similar) Neutrino free streaming erases structure on scales smaller than free streaming distance For neutrino to be dark matter it must have short free streaming length: low temperature or high mass We can put lower limit on mass given T model One possibility to postulate a sterile neutrino that is created through mixing from active neutrinos. This is natural in a 3 right handed neutrinos setting, two are used to generate mass for LH, 3rd can be dark matter. To act like CDM need high mass, >keV. To suppress its abundance need small mixing angle,  0.001, never thermalized

66. Sterile neutrino as dark matter A sterile neutrino in keV range could be the dark matter and could also explain baryogenesis, pulsar kicks, seems very natural as we need sterile neutrinos anyways (Dodelson and Widrow, Asaka, Shaposhnikov, Kusenko, Dolgov and Hansen…) However, a massive neutrino decays and in keV range its radiative decays can be searched for in X-rays. If the same mixing process is responsible for sterile neutrino generation and decay then the physics is understood (almost, most of the production happens at 100MeV scale and is close or above QCD phase transition) Strongest limits come from X-ray background and COMA/Virgo cluster X-rays and our own galaxy, absence of signal gives m<3.5- 8keV (Abazajian 2005, Boyarsky etal 2005)

67. Sterile neutrino as dark matter To proceed we need to specify the model: assume no generation of sterile neutrinos above GeV, no lepton asymmetry enhancements, only production through mixing First approximation: production independent of momentum calculations in Abazajian (2005) give more accurate momentum distribution: 10% weaker mass constraints relative to previous calculations which assume momentum distribution is the same as active The limits for this model can be easily modified to other models (mirror, thermal, entropy injection from massive steriles etc)

70. Results and implications Combined with the 6keV (COMA), 8-9keV (Virgo, X-ray background) upper limit from radiative decays THIS model is excluded How do the constraints change with possible entropy injection that dilutes sterile neutrinos relative to CMB photons/active neutrinos? T is decreased relative to CMB, neutrinos are colder Dilution requires larger mixing angle for same matter density, so decay rate higher, which makes X-ray constraints tighter This does not open up the window To solve the model need to generate neutrinos with additional interactions at high energies above GeV

71. Future surveys and issues of statistics Weak lensing: ground (Panstarrs, DES, LSST), space (SNAP, Dune) Cluster surveys: SZ, X-rays, optical BAO: APO-LSS, ADEPT Ly-alpha: nothing dedicated but can be part of a general spectroscopic survey Beyond Fisherology in figure of merit: there is realization noise in error predictions vs reality, more so for nongaussian distributions. Realization noise leads to weakening of predicted power in discriminating between models (because we can be unlucky in the realization)

72. Realization noise In some cases (eg, with positivity requirement) a factor of two difference between Fisher prediction and actual realization One should report the realization noise in figure of merit and two experiments within the error margin should be deemed equal in power We need to focus more on higher sigma contours, 3 and beyond! Slosar and US, in prep

73. Conclusions LSS can probe dark energy through a number of techniques, including galaxy clustering, weak lensing and their cross- correlations, cluster abundance and clustering and Ly-alpha forest Dark energy remarkably similar to cosmological constant, w=-1.04+/- 0.06, no evidence for w evolution (or modified gravity) Best constraints achieved by combining multiple techniques: this is also needed to test robustness of the results against systematics. Future prospects: many planned space and ground based missions, this may lead to a factor of several improvements in dark energy parameters like w, w’. Systematics, systematics, systematics, statistics Much to be learned, but there remains much work to do for everyone involved