Large Scale Cosmic Microwave Background Anisotropies and Dark Energy

TL;DR

This work investigates how a dark energy component with a constant equation of state $w$ and its perturbations influence large-scale CMB anisotropies, emphasizing the integrated Sachs-Wolfe effect. By deriving a general perturbation framework that includes a constant sound speed ${\hat{c}}_s^2$ and using CAMB/CosmoMC to fit CMB+LSS+SNe data, the authors show that including dark-energy perturbations alters parameter degeneracies and weakens the ability of large-scale CMB alone to distinguish models. They find $w \approx -1.02$ (95% C.L. bounds ± depend on data) and no significant constraint on ${\hat{c}}_s^2$, indicating a cosmological-constant–like behavior is consistent with current data but that scalar-field dark energy remains viable. The study highlights the potential of cross-correlations with large-scale structure and future surveys to tighten constraints on dark energy properties, including its sound speed and clustering behavior.

Abstract

In this note we investigate the effects of perturbations in a dark energy component with a constant equation of state on large scale cosmic microwave background anisotropies. The inclusion of perturbations increases the large scale power. We investigate more speculative dark energy models with w<-1 and find the opposite behaviour. Overall the inclusion of perturbations in the dark energy component increases the degeneracies. We generalise the parameterization of the dark energy fluctuations to allow for an arbitrary const ant sound speeds and show how constraints from cosmic microwave background experiments change if this is included. Combining cosmic microwave background with large scale structure, Hubble parameter and Supernovae observations we obtain w=-1.02+-0.16 (1 sigma) as a constraint on the equation of state, which is almost independent of the sound speed chosen. With the presented analysis we find no significant constraint on the constant speed of sound of the dark energy component.

Figures (8)

• Figure 1: The quadrupole ($l=2$) contribution to the integrated Sachs-Wolfe effect. The solid line is for a $\Lambda$CDM universe, the dot dashed line for a universe with $w=-2$ and the dashed line for $w=-0.6$. For the other cosmological parameters see text. The bold lines are including perturbations in the dark energy component and the thin lines excluding them.
• Figure 2: CMB angular power spectra for different dark energy models with no perturbations. The solid line is for a $\Lambda$CDM model, the dotted line for a model with $w=-0.6$ and dashed line $w=-2.0$. The parameters $\Omega_c$, $\Omega_b$ and $H_0$ are adjusted to show the degeneracies as mentioned in the text.
• Figure 3: CMB angular power spectra for them dark energy models as in Fig. \ref{['fig:Clno']}, but with dark energy perturbations.
• Figure 4: Evolution of $|\delta_{\rm de}|$ (thick) and $v_{\rm de}$ (thin) in the frame comoving with the dark matter perturbation (dotted line), for $w=-0.6$ and ${\hat{c}}_s^2 = \{1, 0.7, 0.1\}$ (solid, dashed and dash-dotted lines), and $k=10^{-3} {\rm Mpc}^{-1}$. Note that we plot the absolute values of the fluctuations with amplitude normalized to unit initial curvature perturbation.
• Figure 5: On the left the CMB anisotropies for the $w=-0.6$ model. The top solid line is with perturbations and the low dashed line for no perturbations. In between the speed of sound is decreasing from top to down with $c_s^2 = 0.2,0.05,0.01,0.0$. On the right the CMB anisotropies for the $w=-2.0$ model. The lower solid line is with perturbations and the top dashed line for no perturbations. In between the speed of sound is increasing from top to down with $c_s^2 = 0.0,0.01,0.05,0.2$. The thin dotted lines above (for $w=-0.6$) and below (for $w=-2$) correspond to sound speeds of $c_s^2 = 5.0$. Note that in both cases that $c_s^2 = 1.0$ corresponds to the solid line.