Semiclassical limit and time in quantum cosmology

Abstract

We propose a method to recover the time variable and the classical evolution of the Universe from the minisuperspace wave function of the Wheeler-DeWitt equation. Defining a Hamilton-Jacobi characteristic function W as the imaginary part of the ln Ψ, we can recover the classical solution and the quantum corrections. The key idea is to let the energy of the Wheeler-DeWitt equation vanish only after the semiclassical limit is taken.