  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. But, it exhibits growing models with
respect to scalar perturbations whose maximum occurs in the bouncing. Hence,
large inhomogeneties 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 change essentially the
results. We discuss also a quantum version of the classical repulsive phase,
through the Wheeler-de Witt equation in mini-superspace, and we show that it
displays essentially the same scenario as the corresponding attractive phase.
