Abstract
We consider a homogeneous and isotropic cosmological model with the gravitational and cosmological constants generalized as coupling scalars in the framework of f(R,T) gravity. A general method of finding the exact solutions is established with the conditions satisfying G=G0an and ρ=ρ0a−m. We investigate the behaviors of G and Λ with the evolution of Universe. Both Big Rip and future crunch are observed in this work. In this paper, we also present the a test of the energy conditions of the present model of the Universe and demonstrate that the consistency with the observational data can be achieved.
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