Scalar-tensor cosmologies with dust matter in the general relativity limit

TL;DR

This paper analyzes flat scalar-tensor cosmological models with dust matter near the general relativity limit, deriving analytical solutions to understand the behavior of the scalar field and expansion rate.

Contribution

It provides an analytical approximation scheme for scalar-tensor cosmologies near the GR limit, clarifying the asymptotic behavior of solutions in this regime.

Findings

Solutions asymptotically approach general relativity

Analytical solutions describe scalar field and Hubble parameter dynamics

Implications for cosmological evolution near the GR limit

Abstract

We consider flat Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the energy density of the ordinary dust matter dominates over the energy density of the scalar potential. Motivated by cosmological observations, we apply an approximation scheme in the regime close to the so-called limit of general relativity. The ensuing nonlinear approximate equations for the scalar field and the Hubble parameter can be solved analytically in cosmological time. This allows us to distinguish the theories with solutions that asymptotically converge to general relativity and draw some implications about the cosmological dynamics near this limit.