Gravitação modificada pelos efeitos quânticos e o problema de estabilidade de soluções clássicas

Abstract

In this thesis we look for different aspects of gravitation and the need to make modifications. We start looking for "classic" modifications and then we study the dynamic behavior of metric perturbations in gravity with anomaly-induced quantum corrections. We obtain the equation for gravitational waves in this theory in a homogeneous and isotropic background and then we verify the stability of this with respect to perturbations. We analyze the behavior of perturbations during the inflationary period, the stable phase of the modified Starobinsky inflation, besides the radiation and matter cases. The stability of metric perturbations in higher-derivative gravity theories depends on the energy scale of the initial conditions. We show that, at least in cases of specific cosmological backgrounds, nonphysical massive ghosts that are present in the spectrum of such theories will not "grow-up", remaining in the vacuum state. This will occur until the initial frequency of the perturbations reaches near the Planck energy scale. Thus renormalizable and superrenormalizable theories can be seen as satisfactory effective theories for quantum gravity.