Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic perfect fluid, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on. G may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.