Adiabatic perturbations in coupled scalar field cosmologies

TL;DR

This paper provides a gauge-invariant analysis of perturbations in coupled scalar field cosmologies, focusing on stability issues of adiabatic modes and identifying conditions under which these models remain viable.

Contribution

It introduces a matrix-eigensystem approach to analyze dominant perturbation modes in coupled scalar field models, highlighting stability conditions for adiabatic perturbations.

Findings

Stability of adiabatic modes depends on the potential shape.

Exponential coupling potential can avoid stability issues.

Explicit calculation of dominant modes in specific models.

Abstract

We present a comprehensive and gauge invariant treatment of perturbations around cosmological scaling solutions for two canonical scalar fields coupled through a common potential in the early universe, in the presence of neutrinos, photons and baryons, but excluding cold dark matter. This setup is relevant for analyzing cosmic perturbations in scalar field models of dark matter with a coupling to a quintessence field. We put strong restrictions on the shape of the common potential and adopt a matrix-eigensystem approach to determine the dominant perturbations modes in such models. Similar to recent results in scenarios where standard cold dark matter couples to quintessence, we show that the stability of the adiabatic perturbation mode can be an issue for this class of scalar field dark matter models, but only for specific choices of the common potential. For an exponential coupling potential, a rather common shape arising naturally in many instances, this problem can be avoided. We explicitly calculate the dominant perturbation modes in such scenarios.