Joint cosmology seminar at Tufts:

Tuesday, October 14, 2014, 2:30 pm
Robinson Hall, Room 250
Tufts University
Refreshments at 2:00 in Knipp Library, Room 251

Unitary and non-unitary transitions around a cosmological bounce

Antonin Coutant
MPI Potsdam


In this work, we will discuss the notion of time and unitarity in the vicinity of a bounce in quantum cosmology, that is, a turning point for the scale factor. We start from the Vilenkin interpretation of the solutions of the Wheeler-DeWitt equation. In this approach, unitarity is defined through the conserved current and is by nature an approximate concept. In minisuperspace it amounts to using the scale factor as a time variable. A unitary evolution is recovered when the latter becomes semi-classical enough. Unfortunately, WKB methods drastically fail near a turning point and the scale factor can- not play the role of time in scenarios with a bounce or a recollapsing phase for the universe. In this work, we extend the results of Vilenkin, Massar and Parentani to momentum represen- tation. For this, we investigate the dynamics of matter transitions when using its conjugate momentum as a time. We describe the precise conditions so as to recover unitarity, and hence, a consistent notion of probability. Then we discuss a concrete example in the vicinity of a bounce.