Quantum geometrodynamics of the Bianchi IX model in extended phase space

TL;DR

This paper introduces a gauge-noninvariant quantum geometrodynamics framework for the Bianchi IX universe, enabling a normalizable, time-dependent wave function consistent with observations, contrasting with traditional Wheeler-DeWitt theory.

Contribution

It develops a mathematically consistent, gauge-noninvariant quantum geometrodynamics for closed universes, specifically applied to the Bianchi IX model, with a normalizable wave function and standard probability interpretation.

Findings

Wave function depends on time and is normalizable.

The theory is gauge-noninvariant, aligning with observation conditions.

Contrasts with Wheeler-DeWitt by providing a non-singular, probabilistic quantum description.

Abstract

A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noninvariant and thus consistent with the observation conditions of a closed universe, by that being considerably distinguished from the conventional Wheeler - DeWitt one. For the Bianchi-IX cosmological model it is shown that a normalizable wave function of the Universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Schrodinger equation. The Wheeler - DeWitt quantum geometrodynamics is represented by a singular, BRST-invariant solution to the Schrodinger equation having no property of normalizability.