SEMICLASSICAL GRAVITY AND QUANTUM INFLATION

We review the semiclassical gravity obtained from the Wheeler-DeWitt equation and present the new asymptotic expansion method. We apply the semiclassical gravity to the quantum tunneling period of the universe, It is found that the matter field obeys non-unitary time-dependent Schrodinger equation. We propose that the non-unitarity of matter field leads to a mechanism for the slow roll-over necessary for the inflation during the tunneling period of the universe.