Cosmologies with Energy Exchange

TL;DR

This paper presents a unified mathematical framework for modeling energy exchange between two fluids in an expanding universe, analyzing various solutions and their implications for cosmological phenomena.

Contribution

It introduces a simplified differential equation model for energy exchange in cosmology, encompassing multiple phenomena like vacuum decay and black hole evaporation.

Findings

Power-law solutions act as late-time attractors under certain conditions.

The model unifies different cosmological energy transfer processes.

Effects of energy transfer on universe expansion are explicitly determined.

Abstract

We provide a simple mathematical description of the exchange of energy between two fluids in an expanding Friedmann universe with zero spatial curvature. The evolution can be reduced to a single non-linear differential equation which we solve in physically relevant cases and provide an analysis of all the possible evolutions. Particular power-law solutions exist for the expansion scale factor and are attractors at late times under particular conditions. We show how a number of problems studied in the literature, such as cosmological vacuum energy decay, particle annihilation, and the evolution of a population of evaporating black holes, correspond to simple particular cases of our model. In all cases we can determine the effects of the energy transfer on the expansion scale factor. We also consider the situation in the presence of anti-decaying fluids and so called phantom fluids which violate the dominant energy conditions.