On gravitational fluctuations and the semiclassical limit in minisuperspace models

An attempt is made to go beyond the semiclassical approximation for gravity in the Born-Oppenheimer decomposition of the wave-function in minisuperspace. New terms are included which correspond to quantum gravitational fluctuations on the background metric. They induce a back-reaction on the semiclassical background and can lead to the avoidance of the singularities the classical theory predicts in cosmology and in the gravitational collapse of compact objects.