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

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 (R, T) gravity when only the pressureless fluid is present. In this respect, we focus on the late time solutions of models of the type f (R, T) = R + beta Lambda (-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 (-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 (-T) = 8 pi G(-T)(alpha) in the presence of ultra-relativistic matter.