Scalar-tensor cosmologies: general relativity as a fixed point of the Jordan frame scalar field

TL;DR

This paper investigates scalar-tensor cosmologies, identifying conditions under which these models mimic general relativity and analyzing the stability of these solutions in different cosmological regimes.

Contribution

It provides a dynamical systems analysis of fixed points in scalar-tensor theories, clarifying when they reproduce general relativity and their compatibility with Solar System tests.

Findings

Two types of fixed points identified, both mimic general relativity.

Only one fixed point type satisfies Solar System PPN constraints.

Conditions on coupling function and potential determine fixed point stability.

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 and scrutinize its limit to general relativity. 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.