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

2. 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

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

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

5. 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.

6. 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

7. 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.

8. 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

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

10. 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…

11. 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

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

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

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

15. 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

16. 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.

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

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

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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. Galaxy bias determination
Galaxies are biased tracers of dark matter; the bias is believed to be scale independent on large scales (k< /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

27. 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

28. 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

29. 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

30. 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)

31. 2.5 sigma detection
Consistent with other probes

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

33. Cosmic
complementarity:
Supernovae,
CMB,
and Clusters

34. 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

35. 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

36. 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)

37. Putting it all together
Dark matter fluctuations on Mpc 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

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

39. DE constraints: degeneracies and dimension of parameter space

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

41. Time evolution of equation of state
w remarkably close to -1
Best constraints at z= , 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