A cosmological scenario from the Starobinsky model within the $f(R,T)$ formalism

TL;DR

This paper develops a new cosmological model within the $f(R,T)$ gravity framework, combining the Starobinsky $R+eta R^2$ model with a linear $T$ term, successfully describing universe expansion phases and fitting observational data.

Contribution

It introduces a novel $f(R,T)$ model using the Starobinsky $f(R)$ form plus a linear $f(T)$ term, and demonstrates its ability to replicate cosmic acceleration and deceleration.

Findings

Model predicts transition redshift consistent with observations.

Energy conditions constrain model parameters.

Hybrid expansion law fits universe expansion history.

Abstract

In this paper we derive a novel cosmological model from the $f(R,T)$ theory of gravitation, for which $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. We consider the functional form $f(R,T)=f(R)+f(T)$, with $f(R)$ being the Starobinksy model, named $R+\alpha R^{2}$, and $f(T)=2\gamma T$, with $\alpha$ and $\gamma$ being constants. We show that a hybrid expansion law form for the scale factor is a solution for the derived Friedmann-like equations. In this way, the model is able to predict both the decelerated and the accelerated regimes of expansion of the universe, with the transition redshift between these stages being in accordance with recent observations. We also apply the energy conditions to our material content solutions. Such an application makes us able to obtain the range of acceptability for the free parameters of the model, named $\alpha$ and $\gamma$.