Late-time cosmological evolution of a general class of f(mathsf{R},mathsf{T}) gravity with minimal curvature-matter coupling

Hamid Shabani,Amir Hadi Ziaie

doi:10.1140/epjc/s10052-017-5077-1

Abstract

In this work, we study the late-time cosmological solutions of f(mathsf{R},mathsf{T})=g(mathsf{R})+h(-mathsf{T}) models assuming that the conservation of the energy-momentum tensor (EMT) is violated. We perform our analysis through constructing an autonomous dynamical system for the equations of motion. We study the stability properties of solutions via considering linear perturbations about the related equilibrium points. Moreover, we parameterize the Lagrangian by introducing the parameters m(r) and n(s). These parameters which are constructed out of the functions g(mathsf{R}) and h(-mathsf{T}) play the main role in finding the late-time behavior of the solutions. We find that there exist, in general, three classes of solutions; all models with n>0 include a proper transition from a prolonged matter era to a de Sitter solution. Models with -0.5<n<0 and n'>1, for at least a root of equation n(s)=s-1, include an unphysical dark energy solution preceding an improper matter era. Finally, for n<-1/2 there is a transient accelerated expansion era with -1/2<w^mathrm{{(eff)}}<-1/3 before a de Sitter phase. For all cases, in order to have a long enough matter dominated epoch, the condition m'rightarrow 0^{+} for rlessapprox -1 must hold. We also show that models with a power law dependency i.e., f(mathsf{R},mathsf{T})=mathsf{R}^{beta }+(-mathsf{T})^{alpha } can be observationally motivating for mrightarrow 0^{+} and -0.024<alpha <0.02 and therefore could provide a suitable setting for later investigations.

Highlights

In the context of a particular class of f (R, T) gravity theories, we have discussed the issue of accelerated expansion of the Universe at the late-time cosmological regimes under the assumption that the energymomentum tensor (EMT) conservation is violated
Our attention was concentrated on those models for which the Lagrangian can be chosen with minimal coupling between the geometrical and matter sectors, which we call minimally coupled models and which can be written as f (R, T) = g(R) + h(T)
We used a way of parameterizations of models via introducing the parameters m = Rg (R)/g (R) and r = −Rg (R)/g(R) for the geometrical part of the Lagrangian and n = −Th (−T)/ h(−T) and s = −Th (−T)/ h(−T) for the matter part

Summary

Introduction

Taking into account the conservation of EMT as a basic constraint, the authors have shown that f (R, T) models with a minimal coupling between the geometrical and matter sectors yield the late-time accelerated expansion of the Universe Most of these models lead to the present value for the EoS parameter as w(DE) = −1/2, which is not observationally acceptable. It may be a good idea to explore the cosmological behavior of the model under violation of EMT conservation To this aim, we rewrite the field equation (9) for specific models given by the choice (17) for f (R, T) function, as follows: Rμν. 2−m(8m+3) 2(m+1) m(10m+7) 2(m+1) as compared to the case of pure f (R) gravity, for which the properties depend upon the matter sector of the Lagrangian.7 Another interesting result is that a DE fixed point (P6) solution is obtained within this framework.

A typical curve of n s n

Concluding remarks