Reconstruction of modified f(R, T) with Λ(T) gravity in general class of Bianchi cosmological models

A new class of cosmological models in f(R, T) modified theories of gravity (Harko et al. Phys. Rev. D, 84, 024020 (2011)) where the gravitational Lagrangian is given by an arbitrary function of Ricci scalar R and the trace of the stress-energy tensor T, have been investigated for a specific choice of f(R, T) = f(1)(R) + f(2)(T) in a general class of Bianchi universe. Our intention is to reconstruct f(R, T) models inspired by this special law for the deceleration parameter (Akarsu and Dereli. Int. J. Theor. Phys. 51, 612 (2012)), which is linear in time with negative slope in connection with the theories of modified gravity. In the present study we consider the cosmological constant Lambda as a function of the trace of the stress energy-momentum tensor, and such a model is nicknamed Lambda(T) gravity. Such models may exhibit better consistency with the recent cosmological observations. We analyze the variation of pressure, energy density, and cosmological terms with cosmic time and discuss their physical consequences. We also discuss physical and geometric properties of derived models.