Potential dominated scalar-tensor cosmologies in the general relativity limit: phase space view

TL;DR

This paper analyzes the phase space of potential dominated scalar-tensor cosmologies near the general relativity limit, classifying possible trajectories and identifying conditions for general relativity to act as an attractor.

Contribution

It introduces a nonlinear approximation scheme to study phase trajectories in scalar-tensor cosmologies near the GR limit, providing a complete classification of phase portraits.

Findings

Topology of trajectories indicates when GR is an attractor

Complete classification of phase portraits in scalar-tensor models

Nonlinear approximation reflects full system behavior

Abstract

We consider the potential dominated era of Friedmann-Lemaitre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling functions, and focus upon the phase space of the scalar field. To study the regime suggested by the local weak field tests (i.e. close to the so-called limit of general relativity) we propose a nonlinear approximation scheme, solve for the phase trajectories, and provide a complete classification of possible phase portraits. We argue that the topology of trajectories in the nonlinear approximation is representative of those of the full system, and thus can tell for which scalar-tensor models general relativity functions as an attractor.