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

Genly Leon, A. Paliathanasis, P. G. L. Leach

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.

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 -cosmology. Specifically, for some power-law -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.
Paper Structure (9 sections, 28 equations, 1 table)

This paper contains 9 sections, 28 equations, 1 table.

Table of Contents

  1. Introduction
  2. $f\left( R\right)$-Cosmology
  3. Singularity analysis
  4. Analytic solutions
  5. Model $f\left( R\right) =R^{\kappa}$
  6. Model $f\left( R\right) =R+qR^{\kappa}-2\Lambda$
  7. Model $f\left( R\right) =R+qR^{\kappa}+\beta R^{2}-2\Lambda$
  8. Model $f\left( R\right) =\left( R-2\Lambda\right) ^{\kappa}$
  9. Conclusions