Integrability of anisotropic and homogeneous Universes in scalar-tensor theory of gravitation

TL;DR

This paper introduces a method using Kovalewski exponents to analyze the integrability of anisotropic, homogeneous Universes within scalar-tensor gravity, extending previous relativistic models and classifying their integrability based on these exponents.

Contribution

It develops a novel approach to assess the integrability of cosmological models in scalar-tensor theories using Kovalewski exponents, generalizing the relativistic case.

Findings

Models classified by rationality of exponents

Integrability depends on matter content and model parameters

Framework extends to general scalar-tensor gravity

Abstract

In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in the vacuum and in presence of a barotropic matter fluid, are classified, and their integrability is discussed.