Scalar-tensor cosmologies with a potential in the general relativity limit: time evolution

TL;DR

This paper investigates the time evolution of scalar-tensor cosmological models near the general relativity limit, providing solutions for models approaching GR either exponentially or via damped oscillations, including an example of oscillating dark energy.

Contribution

It offers a nonlinear approximation method for scalar field evolution in scalar-tensor theories near the GR limit, analyzing asymptotic behaviors and providing explicit solutions.

Findings

Models can approach general relativity exponentially or through damped oscillations.

Explicit solutions for scalar field evolution near the GR limit are derived.

An example of oscillating dark energy is presented.

Abstract

We consider Friedmann-Lema\^{\i}tre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.