Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology

TL;DR

This paper discusses the Wheeler-DeWitt equation in quantum cosmology and explores the applicability of a crypto-Hermitian interaction representation, challenging the notion that quantum effects necessarily eliminate the Big Bang singularity.

Contribution

It introduces a novel, hiddenly Hermitian quantum theory framework in the interaction picture to analyze the Wheeler-DeWitt equation in cosmology.

Findings

Supports the possibility of a singularity-preserving quantum cosmology

Proposes a crypto-Hermitian interaction representation as a valid approach

Challenges the belief that quantum effects necessarily resolve the Big Bang singularity

Abstract

Recently, Wang with Stankiewicz (Phys. Lett. B 800 (2020) 135106) opposed the widespread belief that due to quantization, the Big Bang singularity {\em must} necessarily get smeared and replaced by a non-singular "Big Bounce" process. Their claim is supported in a methodically independent manner in which just a highly schematic model (viz., the discrete and drastically simplified Wheeler-DeWitt equation) is considered. Our comparatively elementary argumentation is constructive, based on the assumption that the evolution of the Universe can fully consistently be described using an innovative, hiddenly Hermitian version of quantum theory formulated in a properly upgraded Dirac's interaction picture.