Adiabatic initial conditions for perturbations in interacting dark energy models

TL;DR

The paper addresses the challenge of setting adiabatic initial conditions for perturbations in a phenomenological interacting dark energy model where dark matter decays into dark energy with a constant transfer rate $\Gamma$. It extends the matrix-based approach of Doran et al. to include energy–momentum transfer and derives super-Hubble initial conditions across different early-time dark-energy equations of state $w_e$, identifying viable ranges and instability regimes. A key result is that adiabatic initial conditions for the standard components automatically induce adiabaticity for dark energy when $w_e\le -1$ or $-4/5\le w_e\le 1/3$, while a non-adiabatic blow-up occurs for $-1<w_e<-4/5$ unless $w_{de}$ varies with time. The work provides the necessary initial conditions for Boltzmann solvers and connects to a companion MCMC analysis showing viable cosmologies with a time-varying $w_{de}$, thus enabling robust tests against CMB and large-scale structure data.

Abstract

We present a new systematic analysis of the early radiation era solution in an interacting dark energy model to find the adiabatic initial conditions for the Boltzmann integration. In a model where the interaction is proportional to the dark matter density, adiabatic initial conditions and viable cosmologies are possible if the early-time dark energy equation of state parameter is $w_e > -4/5$. We find that when adiabaticity between cold dark matter, baryons, neutrinos and photons is demanded, the dark energy component satisfies automatically the adiabaticity condition. As supernovae Ia or baryon acoustic oscillation data require the recent-time equation of state parameter to be more negative, we consider a time-varying equation of state in our model. In a companion paper [arXiv:0907.4987] we apply the initial conditions derived here, and perform a full Monte Carlo Markov Chain likelihood analysis of this model.