Dark energy with non-adiabatic sound speed: initial conditions and detectability

TL;DR

This work analyzes a dark-energy fluid with a constant equation of state $w$ and constant sound speed $c_s$, focusing on the initial conditions for perturbations and their detectability with Planck CMB data cross-correlated with LSST-like galaxy maps. The authors derive generalized, non-adiabatic initial conditions and late-time attractor solutions in both synchronous and conformal Newtonian gauges, showing that perturbation evolution becomes largely independent of initial data once attractors are reached. Through full mock likelihood analyses, they find Planck alone cannot detect $c_s$, but Planck plus LSST can constrain the order of magnitude of $c_s$ and exclude $c_s\to0$, with sensitivity depending on $w$ and marginally on $\sum m_\nu$. The results underscore the importance of incorporating attractor dynamics and generalized initial conditions in forecasts and demonstrate realistic prospects for distinguishing dark-energy clustering scenarios with future data.

Abstract

Assuming that the universe contains a dark energy fluid with a constant linear equation of state and a constant sound speed, we study the prospects of detecting dark energy perturbations using CMB data from Planck, cross-correlated with galaxy distribution maps from a survey like LSST. We update previous estimates by carrying a full exploration of the mock data likelihood for key fiducial models. We find that it will only be possible to exclude values of the sound speed very close to zero, while Planck data alone is not powerful enough for achieving any detection, even with lensing extraction. We also discuss the issue of initial conditions for dark energy perturbations in the radiation and matter epochs, generalizing the usual adiabatic conditions to include the sound speed effect. However, for most purposes, the existence of attractor solutions renders the perturbation evolution nearly independent of these initial conditions.

Figures (2)

• Figure 1: The three thick lines show the evolution of the ratio $\delta_x/\delta_\gamma$ in the synchronous gauge, obtained numerically with camb, in a model with: $w=-0.9$, $\hat{c}_s^2 = 0.1$, standard values of the other cosmological parameters, and adiabatic initial conditions for photons, neutrinos, cdm, baryons. We choose the case of a very long wavelength mode ($k=2.3\times 10^{-6}$Mpc$^{-1}$) which remains outside the Hubble radius during all relevant stages: radiation domination (RD), matter domination (MD) and dark energy domination (DED). We integrated this mode starting either: (i) from the "usual initial condition" $\delta_x/\delta_\gamma=(1+w)/(1+w_\gamma)$ with $w_\gamma=1/3$(upper thin horizonal line), which has no physical justification in the synchronous gauge in this context; (ii) from eq. (\ref{['initx']}) (middle thin horizontal line) and (\ref{['initxtheta']}); (iii) from $\delta_x=0$, like in the public version of camb. In each case, the solution quickly evolves in such way to fulfill eq. (\ref{['initx']}) (middle thin horizontal line) during radiation domination, and then eq. (\ref{['suphor']}) (lower thin horizontal line) during matter domination.
• Figure 2: (Top left) Marginalized posterior probability distribution of $\log_{10}[c_s]$ for Planck+LSST and the two fiducial models described in the text and in Table \ref{['table']}, in which $c_s=1$ (red lines) or $c_s=10^{-2}$ (black lines). The dotted lines show the mean likelihood for comparison. (Other plots) For the same models and mock data, joint 68% and 95% confidence contours for $\log_{10}[c_s]$ and the three parameters most correlated to the dark energy sound speed.