The simplest non-minimal matter\u2013geometry coupling in the f(R,\xa0T) cosmology

P H R S Moraes,P K Sahoo

doi:10.1140/epjc/s10052-017-5062-8

Abstract

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.

Highlights

Einstein’s general theory of relativity (GR) has connected the matter content of the universe with the geometry of the fabric of the space-time, through the well-known field equationsGμν = 8π Tμν
Even though geometry and matter are on the same footing, GR does not consider any possible effects of a non-minimal coupling between them
In f (R, T ) gravity theory, the T –dependence is motivated by the consideration of quantum effects and it is well known that quantum field theory in curved space-time yields the possibility of particle production [5,6]

Summary

Introduction

Einstein’s general theory of relativity (GR) has connected the matter content of the universe with the geometry of the fabric of the space-time, through the well-known field equations. There was no product between R and T , or functions of them, in any of the functional forms worked in those references It is the purpose of the present article to explore the cosmological consequences of a nonminimal matter–geometry coupling in f (R, T ) gravity. We write our equations in terms of an effective energy-momentum tensor Tμeνff , which is given by the sum of the usual matter energy-momentum tensor Tμν and the dark energy term TμDνE , coming from the matter–geometry coupling predicted in the Theory. With Tμeνff being the effective energy-momentum tensor, Tμν the usual matter energy-momentum tensor and the dark energy term TμDνE , coming from the matter–geometry coupling predicted in the present theory, is written as. These values are in accordance with recent observational data [36,37,38]

Energy conditions application and its consequences on cosmological quantities

Discussion