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General Relativity and Quantum Cosmology, gr-qc
Abstract:
In this work, we investigate the notion of time and unitarity in the vicinity
of a bounce in quantum cosmology, that is, a turning point for the scale
factor. Because WKB methods drastically fail near a turning point, the scale
factor cannot play the role of time in such scenarios. We overcome this
difficulty by studying the dynamics of matter transitions when using its
conjugate momentum as a time. We find precise conditions so as to recover
unitarity, and hence, a consistent notion of probability. We then compute
transitions in a concrete example, extract the specific feature of a bounce and
argue about the necessity of the conjugate momentum representation to go beyond
the background field approximation. Our analysis is also equally relevant for a
closed universe undergoing a recollapsing phase.
