Constraints on Dark Energy from CMB Eiichiro Komatsu University of Texas at Austin Dark Energy February 27, 2006

Can CMB Constrain the Nature of Dark Energy? Which DE? Early Dark Energy (Inflaton Field) Intermediate Dark Energy (Tracker Field) Late Dark Energy Prospects for constraining the nature of DE with CMB ONLY is … Not so good for Early DE, if B-mode pol. is not detected. Not so good for Intermediate DE Not so good for Late DE Combination of CMB, LSS & SN is very powerful for constraining all of them (and everyone knows that), but let me try to talk just about CMB for 45 minutes (not so easy these days).

What Can CMB Measure? Baryon-to-photon ratio Sound speed and inertia of baryon-photon fluid Matter-to-radiation ratio Matter-radiation equality “ Radiation ” may include photons, neutrinos as well as any other relativistic components. Angular diameter distance to decoupling surface Peak position in l space ~ (Sound horizon)/(Angular Diameter Distance) Time dependence of gravitational potential Integrated Sachs-Wolfe Effect Primordial power spectrum (Scalar+Tensor) Optical depth

What CMB Measures Amplitude of temperature fluctuations at a given scale, l  Multipole moment l~  Small scalesLarge scales Ang.Diam. Distance Baryon-to- photon Ratio Mat-to- Radiatio n Ratio ISW

CMB to Parameters

Matter-Radiation Ratio More extra radiation component means that the equality happens later. Since gravitational potential decays during the radiation era (free-fall time scale is longer than the expansion time scale during the radiation era), ISW effect increases anisotropy at around the Horizon size at the equality.

Matter,, or Q?

Angular Diameter Distance d A =constant

Error in d A = Error in r s rsrs dAdA

ISW Effect Therefore, one might hope that the ISW would help to break degeneracy between w and the other parameters. However… w=-2 w=-0.6 Weller & Lewis (2003)

Perturbations in DE Dark energy is required to be uniform in space (I.e., no fluctuations) if it is a cosmological constant (w=-1). However, in general dark energy can fluctuate and cluster on large scales when w is not -1. The clustering of DE can … source the growth of potential, compensate the suppression of growth due to a faster expansion rate, and lower the ISW effect. Weller & Lewis (2003) This property makes it absolutely impossible to constraint w with CMB alone, no matter how good the CMB data would be.

CMB-LSS Correlation The same gravitational potential would cause ISW and LSS. Cross-correlation signal is an important cross-check of the existence of dark energy. There are ~2-sigma detections of various correlations: Boughn and Crittenden (2004): WMAP x Radio & X-ray sources Nolta et al. (2004): WMAP x NVSS radio sources Scranton et al. (2003): WMAP x LRGs in SDSS Afshordi et al. (2004): WMAP x 2MASS galaxies But it’s hard! CMB is already signal-dominated on large scales, so nothing to be improved on the CMB side. An all-sky galaxy survey observing 10 million galaxies at 0<z<1 gives only 5-sigma detection (Afshordi 2004).

CMB-WL Correlation Non-linear growth of structure at small scales also provides the ISW signal (a.k.a. RS effect) Would that be observable (ever)? The future lensing experiments would be signal-dominated. A lot of room for CMB experiments to improve at small scales. RS

The RS-WL correlation picks up a time-derivative of the growth rate of structure: a sensitive measure of w Several different source redshifts allow us to do tomography on the time derivatives.

RS-WL Correlation: Prediction Nishizawa & Komatsu (in prep.) Positive Correlation (ISW) Negative Correlation (RS) Assumed CMB experiment: 100deg 2, 1 arcmin resolution, 1uK noise per pixel High S/N!

Summary CMB constraints DE properties via Matter-to-radiation Ratio (useful for constraining Tracker field) Angular Diameter Distance (degeneracy lines in w-h and w-Omega) ISW (not very useful) Massive degeneracy between w and h and matter density makes it absolutely impossible for CMB alone to constrain DE properties. It does not matter how good the CMB data would be. It is essential to combine it with LSS and/or SNe. CMB-WL correlation may serve as an additional test of DE properties. Future small-scale CMB experiments might want to increase their angular resolution to ~1 arcmin level.