Cosmological scaling solutions of non-minimally coupled scalar fields

TL;DR

This paper investigates the existence and stability of cosmological scaling solutions involving non-minimally coupled scalar fields with exponential and inverse power law potentials, revealing conditions for stability and asymptotic behavior.

Contribution

It provides a comprehensive analysis of stability conditions for scalar fields with different potentials and coupling constants in cosmological models.

Findings

Scaling solutions exist for inverse power law potentials independent of coupling.

Scalar fields behave as barotropic fluids when coupling is small.

Numerical examples illustrate theoretical stability and behavior results.

Abstract

We study the existence and stability of cosmological scaling solutions of a non-minimally coupled scalar field evolving in either an exponential or inverse power law potential. We show that for inverse power law potentials there exist scaling solutions the stability of which does not depend on the coupling constant $\xi$. We then study the more involved case of exponential potentials and show that the scalar field will assymptotically behaves as a barotropic fluid when $\xi\ll 1$. The general case $\xi\not\ll 1$ is then discussed an we illustrate these results by some numerical examples.