Algebraic integrability of FRW-scalar cosmologies

TL;DR

This paper investigates the integrability of isotropic cosmological models in general relativity and string theory using Painlevé analysis to determine the presence of solutions with the necessary arbitrary constants.

Contribution

It applies Painlevé analysis to assess the algebraic integrability of FRW-scalar cosmologies, extending the understanding of chaos and solvability in these models.

Findings

Determines conditions for integrability in various cosmological models

Identifies cases where solutions admit Laurent expansions with arbitrary constants

Provides criteria for chaos versus integrability in cosmological dynamics

Abstract

For dynamical systems of dimension three or more the question of integrability or nonintegrability is extended by the possibility of chaotic behaviour in the general solution. We determine the integrability of isotropic cosmological models in general relativity and string theory with a variety of matter terms, by a performance of the Painlev\'{e} analysis in an effort to examine whether or not there exists a Laurent expansion of the solution about a movable pole which contains the number of arbitrary constants necessary for a general solution.