Cosmologies with Energy Exchange
John D. Barrow, T. Clifton
TL;DR
This paper presents a unifying two-fluid energy-exchange model in a flat Friedmann universe, reducing the dynamics to a master equation for the Hubble parameter and deriving exact power-law attractors under broad conditions. It shows how diverse cosmological problems—such as particle annihilation, PBH evaporation, and vacuum decay—are specialty cases of the same framework, and explores extensions to anti-decaying and phantom fluids that reveal oscillatory or altered expansion histories. A key result is the attractor nature of power-law solutions when $A^{2}\ge8B$ and $\delta=B/A^{2}\le1/8$, with the ratio of the two energy densities remaining constant during these epochs. The work thus provides a simple, versatile tool for analyzing interacting-fluid cosmologies and clarifies the stability of scaling solutions across a wide range of physical regimes.
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.