Some remarks about non-minimally coupled scalar field models

TL;DR

This paper extends results on flat FLRW models in scalar-tensor gravity, analyzing scalar fields with arbitrary potentials and couplings, focusing on asymptotic behavior and scaling solutions, supported by numerical evidence.

Contribution

It introduces a straightforward framework for characterizing asymptotic structures in scalar-tensor models with general potentials and couplings, emphasizing scaling solutions.

Findings

Characterization of asymptotic phase space structure.

Conditions for existence of scaling solutions.

Numerical confirmation of theoretical results.

Abstract

Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling functions are considered. Mild assumptions under such functions (differentiable class, number of singular points, asymptotes, etc) are introduced in a straightforward manner in order to characterize the asymptotic structure on a phase space. We pay special attention to the possible scaling solutions. Numerical evidence confirming our results is presented.