Ermakov approach for minisuperspace oscillators

TL;DR

This paper applies the Ermakov invariant method to analyze minisuperspace quantum cosmology models, mapping the Wheeler-DeWitt equation to classical oscillators and exploring scalar field effects and analogies with accelerator physics.

Contribution

It introduces the Ermakov approach to minisuperspace oscillators, providing a novel classical-quantum analysis framework for cosmological models with scalar fields.

Findings

Mapping of Wheeler-DeWitt equation to classical oscillators

Analysis of squeezing features in scalar field models

Discussion of analogies with accelerator physics

Abstract

The WDW equation of arbitrary Hartle-Hawking factor ordering for several minisuperspace universe models, such as the pure gravity FRW and Taub ones, is mapped onto the dynamics of corresponding classical oscillators. The latter ones are studied by the classical Ermakov invariant method, which is a natural aproach in this context. For the more realistic case of a minimally coupled massive scalar field, one can study, within the same type of approach, the corresponding squeezing features as a possible means of describing cosmological evolution. Finally, we comment on the analogy with the accelerator physics