On the Asymptotic Behaviour of Cosmological Models in Scalar-Tensor Theories of Gravity

TL;DR

This paper analyzes the long-term behavior of cosmological models in scalar-tensor gravity theories by leveraging their equivalence to general relativity with a scalar field, focusing on self-similar solutions and attractors.

Contribution

It investigates the asymptotic properties of scalar-tensor cosmologies using conformal transformations, highlighting self-similar models and their role as attractors in the evolution.

Findings

Identification of self-similar scalar-tensor models

Characterization of early-time and late-time attractors

Extension of known results to a broader class of theories

Abstract

We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal transformation and field redefinition. In particular, we investigate the asymptotic behaviour of spatially homogeneous cosmological models in a class of scalar-tensor theories which are conformally equivalent to general relativistic Bianchi cosmologies with a scalar field and an exponential potential whose qualitative features have been studied previously. Particular attention is focussed on those scalar-tensor theory cosmological models, which are shown to be self-similar, that correspond to general relativistic models that play an important r\^{o}le in describing the asymptotic behaviour of more general models (e.g., those cosmological models that act as early-time and late-time attractors).