DENSITY PERTURBATIONS IN THE BRANS-DICKE THEORY

We give here the calculation of density perturbations in a gravitation theory with a scalar field non-minimally coupled to gravity, i.e., th e Brans-Dicke theory of gravitation. The purpose is to show the influe nce of this scalar field on the dynamic behaviour of density perturbat ions along the eras where the equation of state for the matter can be put under the form p = alpha rho, where alpha is a constant. We analys e the asymptotic behaviour of this perturbations for the cases alpha = 0, alpha = -1, alpha = 1/3 and rho = 0. In general, we obtain a decay ing and growing modes. In the very important case of inflation, alpha = -1, there is no density perturbation, as it is well known. In the va cuum phase the perturbations on the scalar field and the gravitational field present growing modes at the beginning of the expansion and dec aying modes at the end of this phase. In the case alpha = 0 it is poss ible, for some negative values of omega, to have an amplification of t he perturbations with a superluminal expansion of the scale factor. We can also obtain strong growing modes for the density contrast for the case where there is a contraction phase which can have physical inter est in some primordial era.