Topology selection through quantum cosmology

Abstract

We argue that in order to obtain causal semiclassical Einstein equation at the stage much later than the planck time, we have to regard the in-in pathintegral formalism as fundamental in quantum cosmology. We then deduce that any classical universe should allow at least one maximal surface. If the natural energy condition holds, this mean that (1) the classical universe should be a wheeler universe, i.e. it start from and end in a singularity, and (2) the possible topologies of classical universe are strongly restricted. The implication of the recent observation of the cosmic microwave background radiation is also discussed.