Wheeler-DeWitt equation and corrections to the inflationary spectrum

In this thesis, within the context of the Wheeler-deWitt (WdW) equation, the quantisation of a minimally coupled inflaton field with constant potential is studied. This model captures significant features of the inflationary evolution. A Gaussian superposition of exact solutions to the homogeneous WdW equation is therefore taken into consideration, and the total wave function of the universe is formally obtained. Such a wave function naturally extends the semiclassical approach. We find interesting features of this state and, more importantly, we show that it may leave imprints in the inflationary power spectrum not present in the standard approach.