Measuring the Speed of Dark: Detecting Dark Energy Perturbations

TL;DR

This work investigates whether dark energy perturbations, encoded by the sound speed $c_s$, leave detectable imprints in the CMB and large-scale structure. It++develops a perturbation framework and analyzes three dark-energy models, including an early-dark-energy (cEDE) class with constant $c_s$, using current data to jointly constrain $c_s$ with other cosmological parameters. For constant-$w$ models, current data do not constrain $c_s$, while in the cEDE scenario a low $c_s$ is mildly favored, potentially mimicking additional dark matter at early times; nonetheless, $\,\Lambda$CDM remains fully consistent. The findings emphasize that dark-energy microphysics and early-time clustering can be probed with present datasets and motivate future measurements to map spatial variations of dark energy.

Abstract

The nature of dark energy can be probed not only through its equation of state, but also through its microphysics, characterized by the sound speed of perturbations to the dark energy density and pressure. As the sound speed drops below the speed of light, dark energy inhomogeneities increase, affecting both CMB and matter power spectra. We show that current data can put no significant constraints on the value of the sound speed when dark energy is purely a recent phenomenon, but can begin to show more interesting results for early dark energy models. For example, the best fit model for current data has a slight preference for dynamics (w(a)\ne-1), degrees of freedom distinct from quintessence (c_s\ne1), and early presence of dark energy (Omega_ de(a<<1)\ne0). Future data may open a new window on dark energy by measuring its spatial as well as time variation.

Figures (11)

• Figure 1: The deviation of the power spectrum of the matter density perturbations (Newtonian gauge) from the $c_s=1$ case is plotted vs. wavenumber $k$. Three regions -- above the Hubble scale (small $k$), below the sound horizon (large $k$), and the transition in between -- can clearly be seen. The models have $w=-0.8$ (deviations will be smaller for $w$ closer to $-1$) and constant sound speed as labeled. For the $c_s=0.1$ case, we also show the result (dashed curve) in terms of the gauge invariant variable $D_g$ as defined in Durrer01 (in that work $\Phi$ is equal to minus our $\phi$). This illustrates that the low $k$ behavior is strongly gauge dependent.
• Figure 2: The equation of state (lower three curves) and sound speed (upper three curves) as a function of scale factor are illustrated for two models. The aether model takes $s=3$ (solid curves) or $s=1$ (dashed curves) and $w_0=-0.99$; the early dark energy density $\Omega_e$ is determined from these parameters. Note that the cEDE model (dotted curves, also taking $w_0=-0.99$, and here setting $c_s=0$) is a close match to the aether model.
• Figure 3: CMB temperature power spectrum for $w=-0.8$ and $c_s=1$, explicitly showing the contribution of the late-time ($z<10$) ISW effect.
• Figure 4: Left panel: CMB temperature power spectrum for $c_s=0$, and its difference from the $c_s=1$ case, are plotted for $w=-0.8$, along with the cosmic variance. Right panel: The signal relative to the noise (here just cosmic variance) is low, with the total summed over all multipoles $S/N \simeq 1.0$. Compensating the difference between the models by varying the other cosmological parameters would make the $S/N$ even smaller.
• Figure 5: The ratio of the dark energy to dark matter density power spectra (Newtonian gauge) is plotted for various values of constant $w$ and $c_s$. Although $c_s=0$ gives dramatically more power on subhorizon scales than $c_s=1$, the direct ratio of the dark energy power to the matter power is negligible.