A transition from a decelerated to an accelerated phase of the universe expansion from the simplest non-trivial polynomial function of T in the f(R,T) formalism

TL;DR

This paper derives analytical cosmological solutions within the $f(R,T)$ gravity framework, demonstrating a transition from decelerated to accelerated universe expansion using a simple polynomial dependence on T.

Contribution

It introduces the simplest non-trivial polynomial form of T in $f(R,T)$ gravity and provides analytical solutions showing a universe transition from deceleration to acceleration.

Findings

Model predicts transition from decelerated to accelerated expansion.

Analytical solutions obtained despite non-linear differential equations.

Supports $f(R,T)$ gravity as a viable explanation for cosmic acceleration.

Abstract

In this work we present cosmological solutions from the simplest non-trivial $T$-dependence in $f(R,T)$ theory of gravity, with $R$ and $T$ standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Although such an approach yields a highly non-linear differential equation for the scale factor, we show that it is possible to obtain analytical solutions for the cosmological parameters. For some values of the free parameters, the model is able to predict a transition from a decelerated to an accelerated expansion of the universe.