Ambiguous power spectrum from a quantum bounce

TL;DR

This paper investigates the ambiguity in the power spectrum of quantum bouncing cosmological models caused by different potential choices, revealing how quantum transformations lead to distinct predictions for initial vacuum fluctuations.

Contribution

It explicitly derives the quantum canonical transformation linking different potentials and analyzes how this ambiguity affects the resulting power spectra in bouncing cosmology.

Findings

One spectral index is nearly universal across the quantum parameter space.

The other spectral index occurs only for a measure-zero set of parameters.

The quantum ambiguity significantly influences the predicted cosmological perturbations.

Abstract

A quantum cosmological bouncing model may exhibit an ambiguity stemming from the nonclassical nature of the background evolution: two classically equivalent theories can produce two qualitatively different potentials sourcing the perturbations. We derive explicitly the quantum canonical transformation involving the quantum background to show how it leads to inequivalent theories. We identify the relevant quantum parameter describing the difference and expand upon the ambiguity by calculating the expected power spectra produced for initial quantum vacuum fluctuations in the contracting phase of both potentials. We find that one spectral index corresponds to all values of this parameter but one, while the other thus represents a set of measure zero.