Overview of Large Scale Structure

Uros Seljak Zurich/ICTP/Princeton/Berkeley/LBL

Hamilton, may 16, 2007

Outline1) Methods to investigate dark energy and

dark matter: galaxy clustering, cluster counts, weak lensing, Lya forest

2) Issues of systematics and statistics3) Current constraints: what have we learned

so far, controversies 4) What can we expect in the future?

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)

Growth of structure by gravityPerturbations can be measured at different epochs:1.CMB z=10002. 21cm z=10-20 (?)3.Ly-alpha forest z=2-44.Weak lensing z=0.3-25.Galaxy clustering z=0-2 Sensitive to dark energy, neutrinos…

CBI ACBAR

Lyman alpha forest

0≈z 3≈z

1088≈z

Scale dependence of cosmological probes

WMAP

Complementary in scale and redshift

SDSS Galaxy clustering

Weak lensing

Cluster abundance

Galaxy and quasar survey400,000 galaxies with redshiftsGalaxy surveys: SDSS and 2dF

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 spectrumLinear regime matter power spectrum

Galaxy power spectrum: shape analysisGalaxy 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

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)Tegmark et al. (2006)

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

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 biasSDSS 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

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.

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A Standard Ruler

• The acoustic oscillation scale depends on the matter-to-radiation ratio (mh2) and the baryon-to-photon ratio (bh2).

• 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 DA(z)! Observer

r = (c/H)zr = DA

Baryonic wigglesBest 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

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.

mh2 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+w0) + 0.137K.

• 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!

Weak Gravitational LensingWeak Gravitational Lensing

Distortion of background images by foreground matter

Unlensed Lensed

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)

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

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 2005Hirata etal 2006

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

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

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 2007previous attempts: Hoekstra etal, Sheldon etal

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

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•2.5 sigma detection

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Consistent with other probes

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

Galaxy Cluster AbundanceDependence on cosmological parameters

{ }8.30 )]log(61.0[exp1

315.0 MzM

M

gdM

d

MdM

dnσ

σ

σ

ρ−−⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

growthfunction

powerspectrum (8, M-r)

JenkinsJenkinset al. 2001et al. 2001

∫∞

×

=

minM dM

dndM

dzd

dV

dzd

dN

comoving volume

masslimit

massfunction

# of clusters per unit area and z:

mass function:

overallnormalization

Hubble volumeN-body simulationsin three cosmologiescf: Press-Schechter

)( 2hM∝ )( 32rhM M∝

Sunyaev Zel’dovich effect

X-ray emission from cluster gas

Optical data: red sequence richness

Weak lensing (future?)

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

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

Ly-alpha forest as a Ly-alpha forest as a tracer of dark matter tracer of dark matter and dark energyand dark energy

Basic model: neutral hydrogen (HI) is determined by ionization Basic model: neutral hydrogen (HI) is determined by ionization balance between recombination of e and p and HI ionization from balance between recombination of e and p and HI ionization from UV photons (in denser regions collisional ionization also plays a UV photons (in denser regions collisional ionization also plays a role), this gives role), this gives

Recombination coefficient depends on gas temperatureRecombination coefficient depends on gas temperature

Neutral hydrogen traces overall gas distribution, which traces dark Neutral hydrogen traces overall gas distribution, which traces dark matter on large scales, with additional pressure effects on small matter on large scales, with additional pressure effects on small scales (parametrized with filtering scale kscales (parametrized with filtering scale kFF))

Fully specified within the model, no bias issues

2gasHI ρρ ∝

SDSS Lya power spectrum analysisMcDonald, 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 fitLy-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

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

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

Partial degeneracy between UV Partial degeneracy between UV background flux and amplitude is background flux and amplitude is broken, factor of 3 improvement in broken, factor of 3 improvement in amplitudeamplitude

Can determine power law slope of the Can determine power law slope of the growth factor to 0.1growth factor to 0.1

Mandelbaum etal 2003Mandelbaum etal 2003

Upcoming analysis on SDSSUpcoming analysis on SDSS

Slosar etalSlosar etal

Will provide a much better amplitude Will provide a much better amplitude and hopefully resolve the amplitude and hopefully resolve the amplitude controversycontroversy

Future of LYA: more data, Future of LYA: more data, nongaussian signal, 3-d analysis, nongaussian signal, 3-d analysis, better modeling and simulations…better modeling and simulations…

Bispectrum: measuring dark energy at z>2

Simulations, not yet real data

Putting it all together

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US etal 04, 06

Dark matter fluctuations on 0.1-10Mpc scale: amplitude, slope, running of the slopeGrowth of fluctuations between 2<z<4 from LyaLya very powerful when combined with CMB or galaxy clustering for inflation (slope, running of the slope), dark energy through growth rate comparison to z<1 data, can also detect it directly if DE is significant for z>2 still important because it is breaking degeneracies with other parameters and because it is determining amplitude at z=3.

Dark energy constraints: complementarity of tracers

US, Slosar, McDonald 2006

Time evolution of equation of state w

Individual parameters very degenerate

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

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)

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

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