Dark energy and the CMB

Dark energy and the CMB Robert Crittenden Work with S. Boughn, T. Giannantonio, L. Pogosian, N. Turok, R. Nichol, P.S. Corasaniti, C. Stephan-Otto

Measurements of CMB anisotropies • Beautiful new data from WMAP and smaller angle experiments • What do they tell us about dark energy?

Why use the CMB to study dark energy? • Naively, dark energy is a late universe effect, while the CMB primarily probes the physics of the last scattering surface. • Extrapolating backwards, the expected energy density of baryons/dark matter is a billion times higher at z=1000, while the dark energy density is about the same. • Thus, we might not expect dark energy would much of an effect on the CMB! • But despite this, it is a very useful tool in DE studies… Matter density Dark energy Radiation density z=1000 Last scattering

Ways the CMB is useful for DE: • Provides an inventory of virtually everything else in the Universe, particularly what is missing! • Acts as a standard ruler on the surface of last scattering with which we can measure the geometry of the Universe. • Some CMB anisotropies are created very recently: • Integrated Sachs-Wolfe effect • Non-linear effects like Sunyaev-Zeldovich • In some dark energy models, like tracking models, the dark energy density can change significantly, so that it is important at z=1000.

What might we learn about DE? • How much of it is there? • Parameterized in terms of its present density • How does it evolve? • What is its equation of state? • How does it cluster? • Smooth on small scales, but might cluster on large scales • Characterized by the DE sound horizon, • Is it really matter or is it modified gravity?

Ways the CMB is useful for DE: • Provides an inventory of virtually everything else in the Universe, particularly what is missing! • Acts as a standard ruler on the surface of last scattering with which we can measure the geometry of the Universe. • Some CMB anisotropies are created very recently: • Integrated Sachs-Wolfe effect • Non-linear effects like Sunyaev-Zeldovich • In some dark energy models, like tracking models, the dark energy density can change significantly, so that it is important at z=1000.

Weighing the universe There must be enough matter to explain the present expansion rate: Dark energy density we’re trying to determine

Weighing the universe There must be enough matter to explain the present expansion rate: • Photon density constraint (0.004 %): • Observed CMB temperature

Weighing the universe There must be enough matter to explain the present expansion rate: • Total matter density (dark matter + baryons): • CMB Doppler peak heights

Weighing the universe There must be enough matter to explain the present expansion rate: • Baryon density constraints: • Light element abundances • CMB Doppler peak ratios

Weighing the universe There must be enough matter to explain the present expansion rate: • Neutrino density constraints (< 1%): • Small scale damping in LSS • Overall neutrino mass limits

Weighing the universe There must be enough matter to explain the present expansion rate: • Curvature of universe constraint (< 2%): • Angular size of CMB structures • Limit depends on dark energy assumptions

Weighing the universe There must be enough matter to explain the present expansion rate: • Critical density constraint: • Measurement of Hubble constant • Biggest source of possible systematic errors

Weighing the universe Bottom line: Much of the uncertainty comes from the late Universe, so an improvement in the Hubble constant measurement would be very useful!

Ways the CMB is useful for DE: • Provides an inventory of virtually everything else in the Universe. • Acts as a standard ruler on the surface of last scattering with which we can measure the geometry of the Universe. • Some CMB anisotropies are created very recently: • Integrated Sachs-Wolfe (ISW) effect • Non-linear effects like Sunyaev-Zeldovich • In some dark energy models, like tracking models, the dark energy density can change significantly, so that it is important at z=1000.

CMB as cosmic yardstick Physical size of acoustic sound horizon The time of recombination and the sound speed are well determined, telling us what this important scale is.

CMB as cosmic yardstick Angular distance to last scattering surface

CMB as cosmic yardstick If we have a small amount of curvature, this will change the observed angular size. This is very hard to distinguish from changes to the angular distance to the last scattering. WMAP figure

CMB as cosmic yardstick The CMB is imprinted with the scale of the sound horizon at last scattering. This characteristic scale is shown by the Doppler peaks. Both the curvature and the dark energy can change the angular size of the Doppler peaks. Assuming a cosmological constant, we get a constraint on curvature. However, if we assume a flat universe, we can find a constraint on the dark energy density and its evolution. WMAP compilation Fix angular scale of sound horizon

CMB as cosmic yardstick WMAP3 results Even including all the other data, a degeneracy remains between the equation of state and a small amount of curvature. The CMB fixes a single integrated quantity and has a fundamental degeneracy between the dark energy density and its equation of state, which can be broken by other observations.

Ways the CMB is useful for DE: • Provides an inventory of virtually everything else in the Universe. • Acts as a standard ruler on the surface of last scattering with which we can measure the geometry of the Universe. • Some CMB anisotropies are created very recently: • Integrated Sachs-Wolfe (ISW) effect • Non-linear effects like Sunyaev-Zeldovich • In some dark energy models, like tracking models, the dark energy density can change significantly, so that it is important at z=1000.

ISW overview What is the ISW effect? Why is it interesting? Detecting the ISW • Examples • X-ray background • SDSS quasars • Present limits • Future measurements Improving the detections Conclusions

Two independent CMB maps The CMB fluctuations we see are a combination of two largely uncorrelated pieces, one induced at low redshifts by a late time transition in the total equation of state. Early map, z~1000 Structure on many scales Sound horizon as yardstick Late ISW map, z< 4 Mostly large scale features Requires dark energy/curvature

Dark energy signature The ISW effect is gravitational, much like gravitational lensing, but instead of probing the gravitational potential directly, it measures its time dependence along the line of sight. potential depth changes as cmb photons pass through gravitational potential traced by galaxy density The gravitational potential is actually constant in a matter dominated universe on large scales. However, when the equation of state changes, so does the potential, and temperature anisotropies are created.

What can the ISW do for us? Independent evidence for dark energy • Shows how DE affects growth of perturbations • Matter dominated universe in trouble Differential measurement of structure evolution • Only arises when matter domination ends! Direct probe of the evolution of structures • Do the gravitational potentials grow or decay? • Constrain modified gravity models? Probes structure formation on the largest scales • Measure dark energy clustering (Bean & Dore, Weller & Lewis, Hu & Scranton)

Modified gravity Modified gravity theories might have very different structure growth. Thus, they lead to very different predictions for ISW even with the same background expansion! Extra dimensional changes typically affect largest scales the most. This is where the predictions are most uncertain. Lue, Scoccimarro, Starkman 03

DGP model On small scales, there is an Anzatz (Koyama & Maartens) for solving for the growth of structure, but things are still uncertain for large scales. In the ISW, this leads to different predictions, particularly at high redshifts where a higher signal could be generated. The signal at low l (l < 20) is still uncertain, though a new anzatz has recently been proposed. (Song, Sawicki & Hu). Song, Sawicki & Hu 06

What can the ISW do for us? Independent evidence for dark energy • Shows how DE affects growth of perturbations • Matter dominated universe in trouble Differential measurement of structure evolution • Only arises when matter domination ends! Direct probe of the evolution of structures • Do the gravitational potentials grow or decay? • Constrain modified gravity models? Probes structure formation on the largest scales • Measure dark energy clustering on horizon scale (Bean & Dore, Weller & Lewis, Hu & Scranton)

How do we detect ISW map? The typical scale is the horizon size, because smaller structures tend to cancel out. On linear scales positive and negative effects equally likely. Difficult to measure directly: • Same frequency dependence. • Small change to spectrum. • Biggest just where cosmic variance is largest. But we can see it if we look for correlations of the CMB with nearby (z < 2) matter! RC & N. Turok 96 SDSS: H. Peiris & D. Spergel 2000

Cross correlation spectrum The gravitational potential determines where the galaxies form and where the ISW fluctuations are created! Thus the galaxies and the CMB should be correlated, though its not a direct template. Most of the cross correlation arises on large or intermediate angular scales (>1degree). The CMB is well determined on these scales by WMAP, but we need large galaxy surveys. Can we observe this? Yes, but its difficult!

Fundamental problem While we see the CMB very well, the usual signal becomes a contaminant when looking for the recently created signal. Effectively we are intrinsically noise dominated and the only solution is to go for bigger area. But we are fundamentally limited by having a single sky. Noise! Signal ISW map, z< 4 Early map, z~1000

Example: hard X-ray background • XRB dominated by AGN at z ~ 1. • Remove possible contaminants from both: • Galactic plane, center • Brightest point sources • Fit monopole, dipole • Detector time drifts • Local supercluster Hard X-ray background - HEAO-1 CMB sky - WMAP

Cross correlations observed! What is the significance? • Dominated not by measurement errors, but by possible accidental alignments. • This is modeled by correlating the XRB with random CMB maps with the same spectrum. • This gives the covariance matrix for the various bins. Result: 3 detection dots: observed thin: Monte Carlos thick: ISW prediction given best cosmology and dN/dz errors highly correlated S. Boughn & RC, 2004

Could it be a foreground? Possible contaminations: • Galactic foregrounds • Clustered extra-galactic sources emitting in microwave • Sunyaev-Zeldovich effect Tests: • insensitive to level of galactic cuts • comparable signal in both hemispheres • insensitive to point source cuts • correlation on large angular scales • independent of CMB frequency channel

CMB frequency independence Cross correlations for ILC and various WMAP frequency bands lie on top of each other. Not the strong dependence expected for sources emitting in the microwave. Radio-WMAP XRB-WMAP

A few contaminated pixels? The contribution to the correlation from individual pixels pairs is consistent with what is expected for a weak correlation. Correlation is independent of threshold, thus NOT dominated by a few pixels blue: product of two Gaussians red: product of two weakly correlated Gaussians

Highest redshift detection of ISW • To understand the evolution of the potential, its important to push to higher redshifts. • One possible sample is the SDSS quasars (Peiris & Spergel 2000). We use the photometrically selected sample of Richards et al. 2004 • 300,000 objects up to z =2.7. • Covers 16% of the sky. • Some fraction (~5%) are local stars that are hard to distinguish in color space. • Highest mean redshift of all ISW studies so far; objects have individual redshifts! T. Giannantonio, RC, R. Nichol et al - astro-ph/0607572

QSO map We pixelize using HEALPIX, same as WMAP data. We correct those edge pixels which are partially within the SDSS mask, weighting them less. We explore the effects of potential systematics: • Dust extinction • Poor seeing • Bright sources • Sky brightness The largest effect is the extinction, so we cut out the 20% most reddened pixels.

QSO ACF We first calculate the QSO ACF on large scales. • The amplitude of correlations and inferred bias are consistent with earlier measurements (Myers et al.) • A significant correlation is seen on large angles, in excess of what is expected from theory. • This is consistent with the 5% contamination from stars, and provides a useful cross check. Stellar contamination?

QSO-WMAPII CCF The correlation with WMAP ILC is seen at roughly the expected level and angular dependence. • Significance level 2.0-2.5 , depending on masks, etc. A = 0.31 +- 0.14 • Seen to be independent of CMB frequency. • Error bars calculated with 2000 Monte Carlo simulations. • Q map has small residual correlations with stars, but this does not seem to affect its correlation with the QSO sample. • With full SDSS sample, we will break this up into different redshift slices. Highly correlated errors!

Correlations seen in many frequencies! • X-ray background (Boughn & RC) • SDSS quasars (Giannantonio, RC, et al.) • Radio galaxies: • NVSS confirmed by Nolta et al (WMAP collaboration) • Wavelet analysis shows even higher significance (Vielva et al. McEwan et al.) • FIRST radio galaxy survey (Boughn) Infrared galaxies: • 2MASS near infrared survey (Afshordiet al.) Optical galaxies: • APM survey (Folsalba & Gaztanaga) • Sloan Digital Sky Survey (Scranton et al., FGC, Cabre et al.) • Band power analysis of SDSS data (N. Pamanabhan, et al.)

Detections of ISW Correlations seen at many frequencies, covering a wide range in redshift. • All consistent with cosmological constant model, if a bit higher thanexpected. This has made them easier to detect! • Relatively weak detections, and there is covariance between different observations! • Correlations shown at 6 degrees to avoid potential small angle contaminations (e.g. SZ). (Gaztanga et al.) APM SDSS 2mass X-ray/NVSS New!

Scale with comoving distance APM SDSS 2mass X-ray/NVSS QSO Signal declines and moves to smaller scales at higher redshift. We plot the observations for a fixed projected distance.

What does it say about DE? Thus far constraints are fairly weak from ISW alone. • Consistent with cosmological constant model. • Can rule out models with much larger or negative correlations. • Very weak constraints on DE sound speed. Corasantini, Giannantonio, Melchiorri 05 Gaztanaga, Manera, Multamaki 04

Parameter constraints A more careful job is needed! Quantify uncertainties: • Bias - usually estimated from ACF consistently. How much does it evolve over the samples? Non-linear or wavelength dependent? • Foregrounds - incorporate them into errors. • dN/dz - how great are the uncertainties? Understand errors: • To use full angular correlations, we need full covariances for all cross correlations. • Monte Carlo’s needed with full cross correlations between various surveys.

Extended covariance matrix To combine them, we must understand whether and how the various experiments could be correlated: • Overlaps in sky coverage and redshift. • Magnification bias. First efforts have begun to combine (Ryan Scranton & TG): • NVSS • SDSS, LRG & QSO • 2MASS Preliminary results indicate > 5 total signal!

How good will it get? For the favoured cosmological constant the best signal to noise one can expect is about 7-10. This requires significant sky coverage, surveys with large numbers of galaxies and some understanding of the bias. The contribution to (S/N)2 as a function of multipole moment. This is proportional to the number of modes, or the fraction of sky covered, though this does depend on the geometry somewhat. Of course, this assumes we have the right model-- It might be more! RC, N. Turok 96 Afshordi 2004

Future forecasts Ideal experiment : • Full sky, to overcome ‘noise’ • 3-D survey, to weight in redshift (photo-z ok) • z ~ 2-3, to see where DE starts • 107 -108 galaxies, to beat Poisson noise Unfortunately, z=1000 ‘noise’ limits the signal to the 7-10 level, even under the best conditions. Realistic plans: • Short term - DES, Astro-F (AKARI) • Long term - LSST, LOFAR/SKA Pogosian et al 2005 astro-ph/ 0506396

Dark energy and the CMB