Semi-classical predictions of cosmological wave-packets from ridge-lines

TL;DR

This paper introduces ridge-lines to analyze semi-classical predictions from quantum wave-packets in cosmology, revealing more solutions than classical theory and potential deviations due to quantum effects.

Contribution

It proposes a novel method using ridge-lines to study semi-classical predictions in quantum cosmology, comparing approaches and highlighting quantum corrections.

Findings

Semi-classical predictions have more solutions than classical theory.

Quantum corrections can cause deviations from classical solutions.

Ridge-lines provide a new tool for analyzing wave-packets in quantum cosmology.

Abstract

We introduce a concept of ridge-lines to investigate the semi-classical prediction from wave-packets with arbitrary width in conventional quantum mechanics and the Wheeler--DeWitt quantum cosmology. Two primary approaches are applied to the exact calculation of the ridge-lines, namely the contour and the stream approach. Moreover, aspects of these are discussed and compared to other scenarios and approaches, i.e. the narrow WKB wave-packets and the first-derivative test. As the main result, we show that the semi-classical predictions in toy models have more abundant solutions than in the classical theory, and most interestingly they may deviate from classical solutions due to the quantum corrections.