Higher-Derivative $f(R,\Box R, T)$ Theories of Gravity

TL;DR

This paper extends $f(R,T)$ gravity models to include higher derivatives like $ox R$, deriving equations of motion and analyzing cosmological implications, including de Sitter instability and inflation with graceful exit.

Contribution

The paper introduces a new class of $f(R,ox R, T)$ gravity models with higher derivatives, deriving their equations of motion and exploring their cosmological behavior.

Findings

De Sitter solutions are generally unstable in this model.

The model supports an inflationary scenario with a natural graceful exit.

Higher derivative terms influence the stability and inflation dynamics.

Abstract

In literature there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress-energy momentum tensor $T=T_{\mu}^{\mu}$. This type of modified gravity is called as $f(R,T)$ in which $R$ is Ricci scalar $R=R_{\mu}^{\mu}$. We extend manifestly this model to include the higher derivative term $\Box R$. We derived equation of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter solution is unstable for a generic type of $f(R,\Box R, T)$ model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.