Two fluid scenario for dark energy model in Brans-Dicke theory of gravitation

In this paper, we study the evolution of the dark energy parameter in the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and dark energy in the scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 24:925, 1961). A determinate solution is presented using (i) the special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cimento B 74:183, 1983) and (ii) trace free energy momentum tensor of the two fluid. Two cases of interacting and non-interacting fluid (barotropic and dark energy) scenario is considered and general results are obtained. The physical aspects of the results obtained are, also, discussed.