Is There a Super-Selection Rule in Quantum Cosmology?

Abstract

A certain approach to solving the Wheeler-DeWitt equation in quantum cosmology, based on a type of super-selection rule by which negative frequency solutions are discarded, is discussed. In a preliminary analysis: we recall well-known results in relativistic quantum field theory, showing that adopting this approach of super-selection by discarding a sector of the frequencies does not lead to acceptable results. In the area of quantum cosmology, a qualitatively similar result is obtained: we show that by discarding solutions with negative frequencies, which is usually done in order to demonstrate “strong” results on the resolution of the singularity, important physical processes are lost, namely, the existence of cyclic solutions, which, under certain reasonable assumptions, can be interpreted as processes of creation-annihilation at the Planck scale that are typical of any relativistic quantum field theory.