Noncommutative Quantum Cosmology

TL;DR

This paper extends Quantum Cosmology by incorporating phase-space noncommutativity into the Wheeler-DeWitt equation for a Kantowski-Sachs model, revealing how noncommutative parameters influence quantum states of the universe.

Contribution

It introduces a noncommutative phase-space framework into Quantum Cosmology and derives the modified Wheeler-DeWitt equation using the ADM formalism and Seiberg-Witten map.

Findings

Numerical solutions constrain noncommutative parameters.

Noncommutativity in momenta induces damping in the wave function.

Potential relevance for initial universe state selection.

Abstract

One presents a phase-space noncommutative extension of Quantum Cosmology in the context of a Kantowski-Sachs (KS) minisuperspace model. We obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten map. The resulting WDW equation explicitly depends on the phase-space noncommutative parameters, $\theta$ and $\eta$. Numerical solutions of the noncommutative WDW equation are found and, interestingly, also bounds on the values of the noncommutative parameters. Moreover, we conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommutativity can be relevant for a selection of possible initial states for the universe.