Reconstruction of modified $$f(R,T)$$ f ( R , T ) gravity with perfect fluid cosmological models

Abstract

In this paper we present the cosmological viability of reconstruction of an alternative gravitational theory, namely, the modified \(f(R,T)\) gravity, where \(R\) is the Ricci scalar curvature and \(T\) the trace of stress energy momentum tensor. A functional form of \(f(R,T)= R + 2f(T)\) is chosen for the reconstruction in perfect fluid flat Friedmann–Robertson–Walker model. The gravitational field equations contain two fluid sources, one is perfect fluid and other is due to modified \(f(R,T)\) gravity which is to be considered as an exotic fluid. This allows us for derivation and analysis of a set of new cosmological solutions for \(f(R,T)\) gravity by considering these two fluids as a non-interacting. Two known forms of scale factor (de Sitter and power-law) are considered for the explicit and successful reconstruction. The equation of state parameter (EoS) of exotic matter and the effective EoS parameter have been discussed. In de Sitter solution we find that the \(f(R,T)\) fluid behaves as phantom dark energy when the usual matter (perfect fluid) shows the behavior between decelerated phase to accelerated phase. In the absence of usual matter it behaves as a cosmological constant. In case of power -law cosmology two different cases are discussed and analyzed the behavior of different phases of the universe accordingly through the equation of state and density parameters.