Consequences of energy conservation violation: late time solutions of Lambda (mathsf{T}) mathsf{CDM} subclass of f(mathsf{R},mathsf{T}) gravity using dynamical system approach

Hamid Shabani,Amir Hadi Ziaie

doi:10.1140/epjc/s10052-017-4844-3

Abstract

Very recently, Josset and Perez (Phys. Rev. Lett. 118:021102, 2017) have shown that a violation of the energy-momentum tensor (EMT) could result in an accelerated expansion state via the appearance of an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of a violation of the EMT conservation in a particular class of f(mathsf{R},mathsf{T}) gravity when only the pressure-less fluid is present. In this respect, we focus on the late time solutions of models of the type f(mathsf{R},mathsf{T})=mathsf{R}+beta Lambda (-mathsf{T}). As the first task, we study the solutions when the conservation of EMT is respected, and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, that there generally exist two accelerated expansion solutions of which the stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state depends on the model parameters and a de Sitter solution. We present a method to parametrize the Lambda (-mathsf{T}) function, which is useful in a dynamical system approach and has been employed in the model. Also, we discuss the cosmological solutions for models with Lambda (-mathsf{T})=8pi G(-mathsf{T})^{alpha } in the presence of ultra-relativistic matter.

Highlights

These issues have motived people to seek for some other theoretical foundations or at least apply some modifications to the assumed CDM model
In this work we have investigated the cosmological consequences of violation of energymomentum tensor (EMT) conservation for a class of f (R, T) theories of gravity
We have considered both the ultra-relativistic fluid and Dark Matter” (DM) in a spatially flat, homogeneous and isotropic background given by the Friedmann–Lemaître– Robertson–Walker (FLRW) metric

Summary

Introduction

These issues have motived people to seek for some other theoretical foundations or at least apply some modifications to the assumed CDM model. In the background of f (R, T) gravity, we have investigated a linear combination of the Ricci scalar and an arbitrary function of the trace of EMT, i.e., f (R, T) = R + (T) In this model, the Einstein gravity has been modified by a minimally coupled “trace-dependent” cosmological constant. We present the field equations of f (R, T) modified gravity (MG) and discuss the conservation of EMT. We have used R and T(p, u) ≡ gμνTμ(pν, u) as the Ricci curvature scalar and the trace of EMT of pressure-less and ultra-relativistic fluids (for which we get these matters as the total matter content of the Universe), respectively. 282 Page 4 of 14 models as those that respect EMT conservation and those that do not

Models which obey the conservation of EMT

Models which violate the conservation of EMT

Findings

Conclusion