Quantum Cosmology.

If the cosmological evolution is followed back in time, we come to the initial singularity where the classical equations of general relativity break down. This led many people to believe that in order to understand what actually happened at the origin of the universe, we should treat the universe quantum-mechanically and describe it by a wave function rather than by a classical spacetime. This quantum approach to cosmology was originated by DeWitt 1 and Misner 2 , and after a somewhat slow start has become very popular in the last decade or so. The picture that has emerged from this line of development 3 is that a small closed universe can spontaneously nucleate out of " nothing " , where by " nothing " I mean a state with no classical space and time. The cosmological wave function can be used to calculate the probability distribution for the initial configurations of the nucleating universes. Once the universe nucleated, it is expected to go through a period of inflation, which is a rapid (exponential) expansion driven by the energy of a false vacuum. The vacuum energy eventually thermalized, inflation ends, and from then on the universe follows the standard hot cosmological scenario. Inflation is a necessary ingredient in this kind of scheme, since it gives the only way to get from the tiny nucleated universe to the large universe we live in today. In this talk I would like to review where we stand in this programme. Despite the large amount of work in quantum cosmology, we still do not have a " standard model " , and I am sure that you would get a very different picture if this talk were to be given by Stephen