Unitarily inequivalent quantum cosmological bouncing models

Abstract

By quantizing the background as well as the perturbations in a simple one fluid model, we show that there exists an ambiguity in the choice of relevant variables (assuming factor ordering to have been taken care of), potentially leading to incompatible observational physical predictions. There are, in such models, two fundamental ambiguities, a well-known one (factor ordering) which can be removed by an actual choice, and a new one, which depends on the choice of variables themselves. In a classical inflationary background, the exact same canonical transformations lead to unique predictions, so the ambiguity we put forward demands a background with a sufficiently strong departure from classical evolution. The latter condition happens to be satisfied in bouncing scenarios, which may thus be having predictability issues. Inflationary models could evade such a problem because of the monotonic behavior of their scale factor; they do, however, initiate from a singular state which bouncing scenarios aim at solving.