Quantum Stephani Universe in vicinity of the symmetry center

TL;DR

This paper explores quantum and classical aspects of spherically symmetric Stephani cosmological models with scalar fields, demonstrating how specific initial conditions lead to classical-quantum correspondence and unique bound state solutions.

Contribution

It introduces a canonical quantization approach for Stephani universes, analyzing wave packets, initial conditions, and Bohmian mechanics to connect quantum and classical cosmology.

Findings

Wave packets with good classical-quantum correspondence are constructed.

Canonical prescription suppresses quantum potential, aligning quantum and classical results.

Bound state solutions exist for all positive cosmological constants, unlike in FRW models.

Abstract

We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of `canonical' wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wave packets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from de-Broglie Bohm interpretation of quantum mechanics to recover the notion of time and compare the classical and Bohmian results. We exhibit that the usage of the canonical prescription and appropriate choices of expansion coefficients result in the suppression of the quantum potential and coincidence between classical and Bohmian results. We show that, in some cases, contrary to Friedmann-Robertson-Walker case, the bound state solutions also exist for all positive values of the cosmological constant.