Singularity Resolution in Quantum Cosmology via Page-Wootters Formalism

TL;DR

This paper uses the Page-Wootters formalism within quantum cosmology to show that quantum effects resolve the classical big bang singularity by producing a vanishing probability density at zero volume.

Contribution

It demonstrates how the Page-Wootters formalism provides a consistent, relational, and nonsingular quantum description of the big bang in a Bianchi type-I universe.

Findings

Quantum probability density vanishes at zero volume, indicating singularity resolution.

Relational dynamics depend on Gaussian wavepacket parameters.

Quantum correlations are essential for the emergence of relational time.

Abstract

We investigate the problem of classical big bang singularity in a plane-symmetric Bianchi type-I universe within the Wheeler-DeWitt (WDW) framework of quantum gravity. To address the problem of time, we employ the Page-Wootters formalism, which provides a relational notion of dynamics by conditioning the global state on a clock subsystem. Using Misner variables, the WDW equation assumes a Klein-Gordon (KG) type form. Its general solution is constructed as a Gaussian superposition of momentum eigenstates, resulting in an entangled global state between the clock and the remaining subsystem. Within this relational framework, we construct conditional states and obtain the corresponding probability density consistent with the KG-type inner product. The resulting conditional probability density vanishes in the limit of zero volume for all clock values, indicating quantum resolution of the classical singularity. We further show that positivity of the probability density imposes constraints on the admissible clock values, which depend on the parameters of the Gaussian wavepacket. These results highlight the essential role of quantum correlations in the emergence of relational dynamics, and demonstrate that the Page-Wootters formalism provides a consistent and nonsingular probabilistic description of quantum cosmology.