Probing dark energy perturbations: the dark energy equation of state and speed of sound as measured by WMAP

TL;DR

This work treats dark energy as a general fluid characterized by its equation of state $w$ and rest-frame sound speed $\hat{c}_s^2$, and analyzes linear perturbations to assess how dark-energy clustering imprints on the ISW effect and CMB–LSS cross-correlations. Using WMAP large-scale temperature fluctuations and a perturbation framework, the authors derive a modest 1σ bound $\hat{c}_s^2<0.04$ for certain $w$ values, while cross-correlation with NVSS is currently limited by bias and cosmic variance. They argue that future surveys with better bias calibration and larger-scale reach could improve sensitivity to $\hat{c}_s^2$ and thereby probe dark-energy microphysics. Overall, the paper clarifies the ISW-based signatures of dark-energy perturbations and outlines pathways for precision constraints with upcoming observational data.

Abstract

We review the implications of having a non-trivial matter component in the universe and the potential for detecting such a component through the matter power spectrum and ISW effect. We adopt a phenomenological approach and consider the mysterious dark energy to be a cosmic fluid. It is thus fully characterized, up to linear order, by its equation of state and its speed of sound. Whereas the equation of state has been widely studied in the literature, less interest has been devoted to the speed of sound. Its observational consequences come predominantly from very large scale modes of dark matter perturbations (k < 0.01 h.Mpc^{-1}). Since these modes have hardly been probed so far by large scale galaxy surveys, we investigate whether joint constraints that can be placed on those two quantities using the recent CMB fluctuations measurements by WMAP as well as the recently measured CMB large scale structure cross-correlation. We find only a tentative 1$sigma$ detection of the speed of sound, from CMB alone, c_{s}^{2}<0.04 at this low significance level. Furthermore, the current uncertainties in bias in the matter power spectrum preclude any constraints being placed using the cross correlation of CMB with the NVSS radio survey. We believe however that improvements in bias through improved survey scales and depths in the near future will improve hopes of detecting the speed of sound.

Figures (7)

• Figure 1: Relative suppression of dark energy perturbations to those in CDM as one increases $\hat{c}_{s}^{2}$ from 0 to 1 (top to bottom in both panels) for $w=-0.8$. The top panel shows perturbations in CDM rest frame, which due to entropy perturbations can become negative. The bottom panel shows perturbations in dark energy rest frame which are always positive but for $w<0$ are a fraction of the CDM perturbations. $h$ and $\Omega_{x}$ are fixed so as to fit the WMAP constraints on $\Omega_{b}h^{2}, \Omega_{c}h^{2}$ and angular diameter distance to last scattering Spergel03.
• Figure 2: Evolution the ISW source term, in comparison to the $\hat{c}_{s}^{2}=0$ scenario, with $w=-0.3$, for $\hat{c}_{s}^{2} = 0.25, 0.5, 0.75$ and 1 from bottom to top. $h$ and $\Omega_{x}$ are fixed as in Fig. \ref{['fig1']}.
• Figure 3: CMB TT spectra for $w=-0.3$ (top panel) and $w=-0.9$ (bottom panel) with $\hat{c}_{s}^{2}=0$ and 1, all other parameters fixed to give the best fit at smaller scales. All spectra are normalized to $C_{87}$ for comparison.
• Figure 4: Likelihood contour plot for the dark energy component in the $w-c_{s}^ {2}$ plane showing 1, 2 and 3$\sigma$ contours (heaviest to faintest lines respectively) after marginalising over the power spectrum normalisation .
• Figure 5: Matter power spectra spectra COBE normalised Top panel: $w=-0.9$ (dashed) and $-0.3$ (full) with $c_s^2=0$ and $1$ (top and bottom lines respectively ) Bottom panel: $c_s^2=0$, $w=-1,-0.75,-0.5,-0.25$ from top to bottom (at large scales on both plots)