Cosmological Constant and Noncommutativity: A Newtonian point of view

TL;DR

This paper explores how noncommutative geometry affects Newtonian cosmology, revealing modifications to particle trajectories, violations of the cosmological principle, and connections to G"odel-type metrics, especially with a positive cosmological constant.

Contribution

It introduces a Newtonian cosmological model incorporating noncommutativity, showing novel trajectory behaviors and links to G"odel-type spacetime in certain limits.

Findings

Test particle trajectories are modified by noncommutativity.

The cosmological principle is violated in the noncommutative model.

Spiral trajectories and corrections to the Hubble constant are observed.

Abstract

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a positive cosmological constant, spiral trajectories are obtained and corrections to the Hubble constant appear. It is also shown that, in the limit of a strong noncommutative parameter, the model is closely related to a particle in a G\"odel-type metric.