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 $n=4/3$.

arXiv comment6 pages, discussion improved, to be published in Phys. Lett. A

References in corpus (16)

• f(R) Theories Of Gravity
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Curvature Quintessence
• 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
• Cosmological dynamics of R^n gravity
• Dark energy from modified gravity with Lagrange multipliers
• Constraints and analytical solutions of $f(R)$ theories of gravity using Noether symmetries
• Integrable Scalar Cosmologies I. Foundations and links with String Theory
• Integrable cosmological models with non-minimally coupled scalar fields
• $f(R)$-gravity from Killing Tensors
• Noether symmetric minisuperspace model of $f(R)$ cosmology
• Using Noether symmetries to specify f(R) gravity

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