Some FRW models with variable <b> <i>G</i> </b> and

Abstract

Einstein's field equations with G and both varying with time are considered in the context of general homogeneous, isotropic universes in a way which conserves the energy momentum tensor of the matter content. It is found that the solutions of the field equations, which are based on the variation of as but with different constants of proportionality, describe significantly different cosmological scenarios. It is also found that the non-static models with constant density having a vacuum-like equation of state are endowed with inflation for a wide class of functions G(t) and and a static universe with constant density without the vacuum-like equation of state, can exist only for k = 1 with constant G and .