Observational limits on dark energy Uros Seljak Zurich/ICTP/Princeton Florence, september 4, 2006

Contents of the universe (from current observations)                                                                                        Baryons (4%) Dark matter (23%) Dark energy: 73% Massive neutrinos: 0.1% Spatial curvature: very close to 0

How to test dark energy? Classical tests: redshift- luminosity distance relation (SN1A etc), redshift-angular diameter distance, redshift-Hubble parameter relation

Classical cosmological tests (in a new form) Friedmann’s (Einstein’s) equation

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 trec affects late-time amplitude.

Acoustic Oscillations in the Matter Power Spectrum Peaks are weak; suppressed by a factor of the baryon fraction. Higher harmonics suffer from Silk damping. Requires large surveys to detect! Possible Detection by Miller. Detection would be a confirmation of gravitational structure formation. It *must* be there. Linear regime matter power spectrum

A Standard Ruler Yields H(z) and DA(z)! dr = DAdq dr = (c/H)dz Observer dr = (c/H)dz dr = DAdq The acoustic oscillation scale depends on the matter-to-radiation ratio (Wmh2) and the baryon-to-photon ratio (Wbh2). 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)! The acoustic oscillations are also quantitatively useful, because they can form a standard ruler.

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

How to test dark energy? Classical tests: redshift-distance relation (SN1A etc)… Growth of structure: CMB, Ly-alpha, weak lensing, clusters, galaxy clustering

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

Evidence from Cosmic Microwave Background Radiation (CMB) CMB is an almost isotropic relic radiation of T=2.725±0.002 K CMB is a strong pillar of the Big Bang cosmology It is a powerful tool to use in order to constrain several cosmological parameters The CMB power spectrum is sensitive to several cosmological parameters

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

Determining Basic Parameters Baryon Density Wbh2 = 0.015,0.017..0.031 also measured through D/H

Determining Basic Parameters Matter Density Wmh2 = 0.16,..,0.33

Determining Basic Parameters Angular Diameter Distance w = -1.8,..,-0.2 When combined with measurement of matter density constrains data to a line in Wm-w space

Current 3 year WMAP analysis/data situation Current data favor the simplest scale invariant model TT Run through the regimes.. Sachs Wolfe plateau Acoustic peaks region Damping tail How much do Acbar and CBI tell us? Polarization: Two effects one comes from the decoupling surface. One comes from the reionization of the universe.

Weak Gravitational Lensing Distortion of background images by foreground matter Unlensed Lensed

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

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

Possible sources of systematic error 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 Intrinsic correlations STEP2 project bottom line: current acccuracy at 5% level, plenty of work to do to reach 1% level, not clear 0.1% even possible

Shear-intrinsic (GI) correlation Hirata and US 2004 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 Lensing shear Tidal stretch

Intrinsic correlations in SDSS Mandelbaum, Hirata, Ishak, US etal 2005 300,000 spectroscopic galaxies No evidence for II correlations Clear evidence for GI correlations on all scales up to 60Mpc/h Gg lensing not sensitive to GI

Implications for future surveys Mandelbaum etal 2005, Hirata and US 2004 Up to 30% for shallow survey at z=0.5 10% for deep survey at z=1: current surveys underestimate s8 More important for cross-redshift bins

SDSS 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

Are galaxy surveys consistent with each other? Some claims (eg 2dF analysis) that SDSS main sample gives more than 2 sigma larger value of W Fixing h=0.7 SDSS LRG photo 2dF SDSS main spectro Bottom line: no evidence for discrepancy, new analyses improve upon SDSS main

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 s8 High accuracy determination of s8 is important for dark energy constraints Weak lensing is the most direct method

galaxy-galaxy lensing dark matter around galaxies induces tangential distortion of background galaxies: extremely small, 0.1% Important to have redshifts of foreground galaxies: SDSS (McKay etal 02, Sheldon etal 03,04, Seljak etal 04) Express signal in terms of projected surface density and transverse r Signal as a function of galaxy luminosity

dark matter corr function On large scales galaxies trace dark matter G-g lensing in combination with LRG autocorrelation analysis gives projected dark matter corr. function No issue with intrinsic alignment shear interference

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 Future detections could be up to 6(10?) sigma, not clear if this probe can play any role in cosmological parameter determination

WMAP-SDSS cross-correlation: ISW. N. Padmanabhan, C 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)

2.5 sigma detection Consistent with other probes

Counting Clusters of Galaxies Sunyaev Zel’dovich effect X-ray emission from cluster gas Weak Lensing Simulations: growth factor

Cosmic complementarity: Supernovae, CMB, and Clusters

Ly-alpha forest as a tracer of dark matter 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 kF) Fully specified within the model, no bias issues

SDSS Lya power spectrum analysis McDonald etal 2004 Combined statistical power is better than 1% in amplitude, comparable to WMAP 2<z<4 in 11 bins 2 ≈ 129 for 104 d.o.f. A single model fits the data over a wide range of redshift and scale

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)

Putting it all together 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), not directly measuring dark energy unless 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. US etal 04, 06

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

DE constraints: degeneracies and dimension of parameter space

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 z=0.2-0.3, robust against adding more terms, error the same as for constant w Lya helps because there is no evidence for dark energy at z>2