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

TL;DR

This paper uses singularity analysis to identify parameter values in a specific higher-order gravity model where the equations are integrable, aiding in understanding the model's physical viability.

Contribution

It applies singularity analysis to the $f(R) = R + q R^n$ gravity model to determine parameter conditions for integrability, a novel approach in this context.

Findings

Identifies parameter ranges for integrability in the $f(R)$ gravity model.

Analyzes the special case of $n=4/3$ for integrability.

Provides conditions under which the model's equations are solvable.

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 $f(R) = R + qR^{n}$ 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 $n = 4/3$.