The Adiabatic Instability on Cosmology's Dark Side

Abstract

We consider theories with a nontrivial coupling between the matter and dark energy sectors. We describe a small scale instability that can occur in such models when the coupling is strong compared to gravity, generalizing and correcting earlier treatments. The instability is characterized by a negative sound speed squared of an effective coupled dark matter/dark energy fluid. Our results are general, and applicable to a wide class of coupled models and provide a powerful, redshift-dependent tool, complementary to other constraints, with which to rule many of them out. A detailed analysis and applications to a range of models are presented in a longer companion paper.

Figures (1)

• Figure 1: [Bottom] The two component coupled dark energy (CDE) model, with $\lambda =2$ and coupling $C=-20$ with $H_0=70 \, {\rm km} \, {\rm s}^{-1}\, {\rm Mpc}^{-1}$, $\Omega_{b}=0.05$, $\Omega_{c}=0.2$, $\Omega_{co}=0.05$, and $\Omega_{V}=0.70$. At late times the scalar field finds the adiabatic minimum with asymptotic equation of state, and sound speed $= -1/(1+\gamma) = -0.89$, able to reproduce a viable background evolution consistent with supernovae, CMB angular diameter distance and BBN expansion history constraints. The figure shows the evolution of the effective equation of state, $w_{eff} = P_{tot}/\rho_{tot}=(2/3) (d\ln t / d\ln a) -1,$ (black full line), adiabatic speed of sound, $c_{a}^{2}=\dot{P}_{tot}/\dot{\rho}_{tot}$, (blue long dashed line) and effective speed of sound for $c_s^2=\delta P_{tot}/\delta\rho_{tot}$ at $k=0.01/Mpc$ (red dot-dashed line). The effective equation of state for a comparable $\Lambda$CDM model with $\Omega_{c}=0.25$, $\Omega_b=0.05$ and $\Omega_{\Lambda}=0.7$ is also shown (black dashed line). [Top] The growth of the fractional over-density $\delta=\delta\rho/\rho$ for $k=0.01/Mpc$ for the coupled CDM component, $\delta_{co}$, (red long dashed line) and uncoupled component, $\delta_{c}$, (black full line) in comparison to the growth for the $\Lambda$CDM model (black dashed line). At late times the adiabatic behavior triggers a dramatic increase in the rate of growth of both uncoupled and coupled components, leading to structure predictions inconsistent with observations.