On a Quantum Universe Filled with Yang - Mills Radiation

TL;DR

This paper explores a quantum cosmological model with a Yang-Mills field, analyzing the Wheeler-DeWitt equation, the interpretation of its wave function, and the behavior during inflation, linking quantum and classical descriptions.

Contribution

It introduces a quantum mini-universe model with a Yang-Mills field and discusses the interpretation of the wave function and gauge invariance in quantum cosmology.

Findings

Wave function interpretation via the correspondence principle.

Gauge-invariant measure in mini-superspace.

Behavior of the wave function during inflation.

Abstract

We investigate the properties of a quantum Robertson - Walker universe described by the Wheeler -- DeWitt equation. The universe is filled with a quantum Yang -- Mills uniform field. This is then a quantum mini copy of the standard model of our universe. We discuss the interpretation of the Wheeler -- DeWitt wave function using the correspondence principle to connect $\vert\psi\vert^2$ for large quantum numbers to the classical probability for a radiation dominated universe. This can be done in any temporal gauge. The correspondence principle determines the Schr\"odinger representation of the momentum associated to the gravitational degree of freedom. We also discuss the measure in the mini--superspace needed to ensure invariance of the quantum description under change of the temporal gauge. Finally, we examine the behaviour of $\vert\psi\vert^2$ in inflationary conditions.