Analytical solutions in $R+q{R}^n$ cosmology from singularity analysis

Abstract

The integrability of higher-order theories of gravity is of importance in the determining the properties of these models and so their viability as models of reality. An important tool in the establishment of integrability is the singularity analysis. We apply this analysis to the case of fourth-order theory of gravity $f(R)=R+q{R}^n$ to establish those values of the free parameters $q$ and $n$ for which integrability in this sense exists. As a prelininary we examine the well-known case of $n=4/3$.

6 pages, discussion improved, to be published in Phys. Lett. A

References in corpus (5)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Conditions for the cosmological viability of f(R) dark energy models
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
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• Analytic Solution of the Starobinsky Model for Inflation
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• (Compactified) black branes in four dimensional f(R)-gravity
• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector