Evolutionary quantum cosmology in a gauge-fixed picture

TL;DR

This paper explores classical and quantum models of flat FRW cosmology with a perfect fluid, demonstrating how quantum effects might resolve classical singularities using gauge-fixed Lagrangians and Schrödinger equations.

Contribution

It introduces a gauge-fixed Lagrangian approach to quantum cosmology, deriving a Schrödinger equation for the universe and analyzing singularity avoidance.

Findings

Classical models show power-law expansion with big-bang and big-rip singularities.

Quantum wave functions suggest potential avoidance of classical singularities.

Gauge-fixed approach yields a Schrödinger equation for quantum cosmology.

Abstract

We study the classical and quantum models of a flat Friedmann-Robertson-Walker (FRW) space-time, coupled to a perfect fluid, in the context of the consensus and a gauge-fixed Lagrangian frameworks. It is shown that, either in the usual or in the gauge-fixed actions, the evolution of the universe based on the classical cosmology represents a late time power law expansion, coming from a big-bang singularity in which the scale factor goes to zero for the standard matter, and tending towards a big-rip singularity in which the scale factor diverges for the phantom fluid. We then employ the familiar canonical quantization procedure in the given cosmological setting to find the cosmological wave functions in the corresponding minisuperspace. Using a gauge-fixed (reduced) Lagrangian, we show that, it may lead to a Schr\"{o}dinger equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the time dependent wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.