On the consistency of a repulsive gravity phase in the early Universe

We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the 'wrong sign' for the energy and negative curvature for the spatial section, is studied in detail. The background solutions display a bouncing, non-singular Universe. The model is well behaved with respect to tensor perturbations. However, it exhibits growing models with respect to scalar perturbations whose maximum occurs in the bouncing. Hence, large inhomogeneities are produced. At least for this case, a repulsive phase may destroy homogeneity, and in this sense it may be unstable. A Newtonian analogous model is worked out; it displays qualitatively the same behaviour. The generality of this result is discussed. In:particular, it is shown that the addition of an attractive radiative fluid does not essentially change the results. We also discuss a quantum version of the classical repulsive phase, through the Wheeler-DeWitt equation in minisuperspace, and we show that it displays essentially the same scenario as the corresponding attractive phase.