Abstract

A detailed analysis of a quantum cosmological model based on general relativity coupled to conformal matter (a perfect radiation fluid and conformally coupled scalars) is presented, which shows how the universe undergoes a nonsingular “perfect bounce”. This bounce can be described by a path in the complex plane for the scale factor, similar to a well-known description of quantum tunnelling in complex time. In the case of FRW symmetry, the path integral and transition amplitudes can be computed exactly. For an anisotropic Bianchi I model, we give the general solution to the Wheeler-DeWitt equation and show how to define global positive- and negative-frequency modes which interpolate smoothly between negative and positive infinity, again encountering no singular behaviour at the “Big Bang”. Partial results on nonlinear perturbations suggest that the picture can be extended to more general inhomogeneous universes.