Symmetry, Singularities and Integrability in Complex Dynamics IV: Painleve Integrability of Isotropic Cosmologies

TL;DR

This paper uses singularity analysis to determine the integrability of isotropic cosmological models in general relativity and string theory, identifying which models are integrable based on Painlevé criteria.

Contribution

It applies Painlevé analysis to a range of cosmological models, providing a systematic approach to assess their integrability in complex dynamics.

Findings

Some models are proven integrable using the Painlevé test.

Other models require more complex analysis to determine integrability.

The study clarifies the conditions under which cosmological models are integrable.

Abstract

We apply the results of singularity analysis to the isotropic cosmological models in general relativity and string theory with a variety of matter terms. For some of these models the standard Painlev\'{e} test is sufficient to demonstrate integrability or nonintegrability in the sense of Painlev\'{e}. For others of these models it is necessary to use a less algorithmic procedure.