Noncommutative Geometry and Cosmology

TL;DR

This paper explores how noncommutative geometry influences homogeneous cosmological models, revealing that while classical noncommutativity doesn't remove singularities, quantum effects can lead to non-singular, cyclic universes, especially in quantum noncommutative scenarios.

Contribution

It introduces a deformation of minisuperspace variables to study noncommutative effects on cosmology, comparing classical and quantum models using Bohmian trajectories.

Findings

Noncommutativity significantly alters universe evolution.

Quantum effects can produce non-singular, cyclic universes.

Quantum noncommutative models exhibit unique dynamic properties.

Abstract

We study some consequences of noncommutativity to homogeneous cosmologies by introducing a deformation of the commutation relation between the minisuperspace variables. The investigation is carried out for the Kantowski-Sachs model by means of a comparative study of the universe evolution in four different scenarios: the classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative. The comparison is rendered transparent by the use of the Bohmian formalism of quantum trajectories. As a result of our analysis, we found that noncommutativity can modify significantly the universe evolution, but cannot alter its singular behavior in the classical context. Quantum effects, on the other hand, can originate non-singular periodic universes in both commutative and noncommutative cases. The quantum noncommutative model is shown to present interesting properties, as the capability to give rise to non-trivial dynamics in situations where its commutative counterpart is necessarily static.