Adiabatic and entropy perturbations with interacting fluids and fields

TL;DR

This work develops a gauge-invariant framework for linear density perturbations in a flat FRW universe with multiple interacting fluids and scalar fields. It recasts N scalar fields as N kinetic fluids plus one potential fluid and decomposes perturbations into adiabatic and isocurvature modes, yielding a set of coupled first-order evolution equations that include energy and momentum transfer. On large scales, non-adiabatic effects are identified and adiabatic initial conditions are formulated for multi-component systems. The approach unifies fluids and scalar fields, extends previous perturbation theory (Kodama-Sasaki, Mukhanov et al.), and provides a versatile tool for studying reheating, curvaton scenarios, and dark-energy dynamics.

Abstract

We develop a gauge-invariant formalism for the study of density perturbations in a Friedmann-Robertson-Walker universe with multiple interacting fluids and/or scalar fields. We show how N scalar fields may be described by N kinetic fluids (with maximally stiff equation of state) interacting with a non-dynamical potential (with vacuum equation of state). We split generic perturbations into adiabatic and entropic parts, and give the coupled first-order evolution equations on all scales, including energy and momentum exchange. We identify the non-adiabatic effects on large scales, and define adiabatic initial conditions in the presence of multiple fluids and fields.