Dynamical symmetries in Brans-Dicke cosmology

TL;DR

This paper uses symmetries in Brans-Dicke cosmology to identify specific scalar field potentials that lead to integrable models and can produce cosmic acceleration with stable de-Sitter solutions.

Contribution

It introduces a method to determine scalar potentials via Killing tensors and contact symmetries, revealing four integrable potentials with cosmological relevance.

Findings

Identified four scalar potentials with exact integrability.

Found conditions for stable de-Sitter late-time attractors.

Demonstrated potentials can produce cosmic acceleration.

Abstract

In the context of generalised Brans-Dicke cosmology we use the Killing tensors of the minisuperspace in order to determine the unspecified potential of a scalar-tensor gravity theory. Specifically, based on the existence of contact symmetries of the field equations, we find four types of potentials which provide exactly integrable dynamical systems. We investigate the dynamical properties of these potentials by using a critical point analysis and we find solutions which lead to cosmic acceleration and under specific conditions we can have de-Sitter points as stable late-time attractors.