Constraining dark energy with cross-correlated CMB and Large Scale Structure data

TL;DR

The paper assesses whether the Integrated Sachs-Wolfe effect, detected via CMB–LSS cross-correlation, can constrain dark energy properties in a flat universe. It develops the ISW cross-correlation formalism, highlighting how the signal depends on the equation of state $w$ and the dark energy sound speed $c_e^2$, with distinct degeneracy directions for $c_e^2=1$ and $c_e^2=0$. Using a likelihood analysis of current cross-correlation data (plus SN-Ia), it finds weak constraints on constant $w$ for $c_e^2=1$ and tighter bounds for clustered dark energy with $c_e^2=0$, while the sound speed remains unconstrained; slowly varying $w(a)$ models are only weakly constrained. The study concludes that upcoming deep redshift surveys will substantially improve ISW-based constraints on dark energy, offering an independent probe alongside CMB and SN-Ia data. $${}$

Abstract

We investigate the possibility of constraining dark energy with the Integrated Sachs Wolfe effect recently detected by cross-correlating the WMAP maps with several Large Scale Structure surveys. In agreement with previous works, we found that, under the assumption of a flat universe, the ISW signal is a promising tool for constraining dark energy. Current available data put weak limits on a constant dark energy equation of state w. We also find no constraints on the dark energy sound speed c_e^2. For quintessence-like dark energy (c_e^2=1) we find w<-0.53, while tighter bounds are possible only if the dark energy is ``clustered'' (c_e^2=0), in such a case -1.94<w<-0.63 at 2-sigma. Better measurements of the CMB-LSS correlation will be possible with the next generation of deep redshift surveys. This will provide independent constraints on the dark energy which are alternative to those usually inferred from CMB and SN-Ia data.

Figures (7)

• Figure 1: Angular cross-correlation function for $c_e^2=1$ (a) and $c_e^2=0$ (b), the different lines corresponds to $w=-0.8$ (solid), $w=-0.4$ (long dash-dot) and $w=-4$ (short dash). Amplitude of the angular cross-correlation at the plateau as function of $w$ for $c_e^2=1$ (c) and $c_e^2=0$ (d).
• Figure 2: Amplitude of the angular cross-correlation at the plateau as function of the redshift. A Gaussian selection function with width $\sigma_{\phi}=0.05$ has been used. The different lines correspond to models as in Figure \ref{['crossz0.1']}.
• Figure 3: Two-dimensional marginalized likelihoods on $\Omega_{DE}-w$. The yellow and red area correspond to $1$ and $2\sigma$ limits inferred from the ISW data for $c_e^2=1$. Solid and dash lines represent the $1$ and $2\sigma$ contours from the SN-Ia data.
• Figure 4: As in Figure \ref{['olwcs1']} with $c_e^2=0$ prior.
• Figure 5: Dots with errorbars are the different measurements of $\bar{C}^X/b$, the solid line corresponds to the LCDM best fit model, the long-dash and short-dash lines show the case ($w=-0.2,\Omega_{DE}=0.7$) and ($w=-2,\Omega_{DE}=0.6$) respectively.