Quantum cosmological solutions: their dependence on the choice of gauge conditions and physical interpretation

TL;DR

This paper explores how different gauge choices in quantum cosmology affect solutions and their physical interpretation within the extended phase space approach, emphasizing the evolution of wave functions in isotropic models.

Contribution

It provides numerical solutions for various gauge conditions in quantum geometrodynamics, highlighting the impact of gauge choice on physical interpretations and extending previous discussions.

Findings

Solutions depend on gauge conditions

Different gauges yield distinct physical interpretations

The approach replaces static Wheeler-DeWitt picture with dynamic evolution

Abstract

In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space" approach belongs to those appeared in the last decade in which, as a result of fixing a reference frame, the Wheeler - DeWitt static picture of the world is replaced by evolutionary quantum geometrodynamics. Some aspects of this approach were discussed at two previous PIRT meetings. We are interested in the part of the wave function depending on physical degrees of freedom. Three gauge conditions having a clear physical meaning are considered. They are the conformal time gauge, the gauge producing the appearance of Lambda-term in the Einstein equations, and the one covering the two previous cases as asymptotic limits. The interpretation and discussion of the obtained solutions is given.