Quantization of FRW universe via gauge-fixed action

TL;DR

This paper explores the quantization of the Friedmann-Robertson-Walker universe with matter, using a gauge-fixed action to construct a consistent quantum framework that allows evolution across singularities.

Contribution

It introduces a gauge-fixed quantization method for the FRW universe with matter, ensuring self-adjoint operators and well-defined evolution through singularities.

Findings

Operators have self-adjoint realizations.

Quantum states exist with well-defined evolution across singularity.

The approach applies to matter with arbitrary equation of state parameter w.

Abstract

This paper is devoted to investigation of the quantum Friedman-Robertson-Walker universe with matter satisfying the equation of state $p=w\rho$, where $w$ is an almost arbitrary constant. The procedure starts with a reduced Lagrangian, which describes the system in a gauge fixed, so that the evolution parameter corresponds to the cosmological time. Then we construct the phase space, which is believed to correspond to the reduced phase space consisting of Dirac's observables. The physically relevant quantities are mapped into operators. We show that the operators have self-adjoint realizations and that there exist quantum states for which the evolution across singularity is well-defined.