Gravitational instability in Newtonian cosmology with varying G

Use is made of McVittie's model for Newtonian Cosmologies with time-varying G as unperturbed Universe, in the study of linear density perturbations. A general equation for the density fluctuation is obtained. In the case with null pressure and G approx. t-1 (Dirac cosmological model) there results that the fluctuation density grows faster than the corresponding case for G constant. It is, however, insufficient to explain the formation of Galaxies. The situation where p not=0 and k=0, in the case of ideal monoatomic gas, leads only to oscillating solutions. Finally, a model that 'approximates' a particular solution of Brans-Dicke theory leads to a perturbation that differs slightly from classical or relativistic ones, although insufficient for the applications above mentioned. (Author)