Radiation-Dominated Quantum Friedmann Models

TL;DR

This paper quantizes radiation-filled Friedmann universes using the ADM formalism, analyzing both open and closed models, and demonstrates that all models are nonsingular with certain classical features emerging from quantum conditions.

Contribution

It introduces a consistent quantization approach for open and closed radiation-dominated universes, addressing boundary conditions and self-adjointness issues not previously explored.

Findings

All models are nonsingular.

Closed universe predicts infinite radius and Ω=1.

Quantum stationary geometries exist for closed models.

Abstract

Radiation-filled Friedmann-Robertson-Walker universes are quantized according to the Arnowitt-Deser-Misner formalism in the conformal-time gauge. Unlike previous treatments of this problem, here both closed and open models are studied, only square-integrable wave functions are allowed, and the boundary conditions to ensure self-adjointness of the Hamiltonian operator are consistent with the space of admissible wave functions. It turns out that the tunneling boundary condition on the universal wave function is in conflict with self-adjointness of the Hamiltonian. The evolution of wave packets obeying different boundary conditions is studied and it is generally proven that all models are nonsingular. Given an initial condition on the probability density under which the classical regime prevails, it is found that a closed universe is certain to have an infinite radius, a density parameter $\Omega = 1$ becoming a prediction of the theory. Quantum stationary geometries are shown to exist for the closed universe model, but oscillating coherent states are forbidden by the boundary conditions that enforce self-adjointness of the Hamiltonian operator.