Unitary evolution of the quantum universe with a Brown-Kuchar dust

TL;DR

This paper demonstrates that in quantum cosmology with Brown-Kuchar dust, the universe's wave function evolves unitarily, avoiding singularities and exhibiting a big bounce, with classical behavior emerging at late times.

Contribution

It introduces a framework where the Wheeler-DeWitt equation admits unitary evolution with a dust clock, ensuring singularity avoidance and a consistent quantum cosmological model.

Findings

Wave function evolution is unitary for all boundary conditions.

Classical behavior emerges at late times in the universe's volume.

Quantum fluctuations diverge despite classical correspondence.

Abstract

We study the time evolution of a wave function for the spatially flat Friedmann-Lemaitre-Robertson-Walker universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchar dust as a matter field in order to introduce a "clock" in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the universe obeys the classical time evolution in the late time but its variance diverges.