Scalar-tensor cosmologies: fixed points of the Jordan frame scalar field

TL;DR

This paper analyzes the phase space of scalar-tensor cosmologies, identifying fixed points that mimic general relativity and examining their compatibility with Solar System constraints.

Contribution

It provides a detailed dynamical systems analysis of fixed points in scalar-tensor cosmologies, including conditions for their stability and physical viability.

Findings

Identifies fixed points corresponding to potential and matter domination.

Determines which fixed points are compatible with Solar System tests.

Analyzes the phase space structure and its implications for cosmological evolution.

Abstract

We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe the details of the phase space geometry. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and matter domination. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points (attractor or other). There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System PPN constraints. The phase space structure should also carry over to the Einstein frame as long as the transformation between the frames is regular which however is not the case for the latter (PPN compatible) fixed point.