Dynamical vacuum energy and phantom divide-line cross in scalar cosmology

In this paper, we study cosmological models in scalar tensor theory of gravity a la Brans-Dicke with a dynamical equation of state parameter, a dynamical effective cosmological constant and a Hubble parameter varying like with and are real positive parameters and is some pending power index. It is observed that the universe is accelerating in time and it is dominated by a decreasing energy density and a vacuum energy density. However the vacuum energy density is increasing logarithmically at early epoch of time and then decaying toward its present positive value at late-time epoch. For specific choices of the free parameters in the theory, it is observed that the phantom divide line is crossed in the presence of a cosmological constant and the universe expands asymptotically a la de-Sitter at very large time. Additional features are discussed as well.