**77**: 480

https://doi.org/10.1140/epjc/s10052-017-5062-8

Regular Article - Theoretical Physics

## The simplest non-minimal matter–geometry coupling in the *f*(*R*, *T*) cosmology

^{1}
Departamento de Física, ITA - Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900, São Paulo, Brazil

^{2}
Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad, 500078, India

^{*} e-mail: moraes.phrs@gmail.com

Received:
28
March
2017

Accepted:
12
July
2017

Published online:
18
July
2017

*f*(*R*, *T*) gravity is an extended theory of gravity in which the gravitational action contains general terms of both the Ricci scalar *R* and the trace of the energy-momentum tensor *T*. In this way, *f*(*R*, *T*) models are capable of describing a non-minimal coupling between geometry (through terms in *R*) and matter (through terms in *T*). In this article we construct a cosmological model from the simplest non-minimal matter–geometry coupling within the *f*(*R*, *T*) gravity formalism, by means of an effective energy-momentum tensor, given by the sum of the usual matter energy-momentum tensor with a dark energy contribution, with the latter coming from the matter–geometry coupling terms. We apply the energy conditions to our solutions in order to obtain a range of values for the free parameters of the model which yield a healthy and well-behaved scenario. For some values of the free parameters which are submissive to the energy conditions application, it is possible to predict a transition from a decelerated period of the expansion of the universe to a period of acceleration (dark energy era). We also propose further applications of this particular case of the *f*(*R*, *T*) formalism in order to check its reliability in other fields, rather than cosmology.

*© The Author(s), 2017*