New analytic solutions in $f\left(R\right)$-Cosmology from Painlevé analysis

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 Painlevé 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.

arXiv comment16 pages, no figures

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