Qualitative dynamics of interacting vacuum cosmologies

TL;DR

This paper analyzes the qualitative dynamics of cosmological models with interacting vacuum and dark matter, identifying fixed points, stability conditions, and the influence of additional fluids like radiation.

Contribution

It provides a phase-space analysis of interacting vacuum cosmologies, discovering new fixed points and tracking solutions with a third fluid, extending previous scalar field models.

Findings

Fixed points correspond to constant energy density fractions.

Existence conditions for fixed points with energy transfer.

Interacting vacuum+matter can track noninteracting radiation.

Abstract

We present a phase-space analysis of the qualitative dynamics cosmologies where dark matter exchanges energy with the vacuum component. We find fixed points corresponding to power-law solutions where the different components remain a constant fraction of the total energy density and given an existence condition for any fixed points with nonvanishing energy transfer. For some interaction models we find novel fixed points in the presence of a third noninteracting fluid with constant equation of state, such as radiation, where the interacting vacuum+matter tracks the evolution of the third fluid, analogous to tracker solutions previously found for self-interacting scalar fields. We illustrate the phase-plane behavior, determining the equation of state and stability of the fixed points in the case of a simple linear interaction model, for interacting vacuum and dark matter, including the presence of noninteracting radiation. We give approximate solutions for the equation of state in matter- or vacuum-dominated solutions in the case of small interaction parameters.