New analytic solutions in $f\left( R\right) $-Cosmology from Painlev\'{e} analysis

TL;DR

This paper uses singularity analysis to explore integrability and find new analytic solutions in specific $f(R)$-cosmology models, providing constraints on parameters and expressing solutions as Laurent expansions.

Contribution

It applies Painlevé analysis to $f(R)$-cosmology, deriving parameter constraints and obtaining new analytic solutions expressed through Laurent series.

Findings

Identified conditions under which $f(R)$-cosmology models are integrable.

Derived new analytic solutions in terms of Laurent expansions.

Established parameter constraints for specific power-law models.

Abstract

Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in $f\left( R\right)$-cosmology. Specifically, for some power-law $f\left( R\right) $-theories of particular interest, we apply the ARS algorithm to prove if the field equations possess the Painlev\'{e} property. Constraints for the free parameters of the power-law models are derived, and new analytic solutions are derived, expressed in terms of Laurent expansions.