Stochastic motion in an expanding noncommutative fluid

TL;DR

This paper models an expanding noncommutative fluid analogous to cosmological geometries, analyzing test particle motion and revealing noncommutative corrections to velocity dispersion, contrasting with previous commutative results.

Contribution

It introduces a noncommutative fluid model based on a (3+1)-D Abelian Higgs framework and studies particle dynamics within this novel setting.

Findings

Noncommutative corrections affect mean squared velocity of particles.

Velocity dispersion remains nonzero in the noncommutative case.

Results differ from previous null findings in commutative expanding fluids.

Abstract

A model for an expanding noncommutative acoustic fluid analogous to a Friedmann-Robertson-Walker geometry is derived. For this purpose, a noncommutative Abelian Higgs model is considered in a (3+1)-dimensional spacetime. In this scenario, we analyze the motion of test particles in this fluid. The study considers a scalar test particle coupled to a quantized fluctuating massless scalar field. For all cases studied, we find corrections due to the noncommutativity in the mean squared velocity of the particles. The nonzero velocity dispersion for particles that are free to move on geodesics disagrees with the null result found previously in the literature for expanding commutative fluid.