Noncommutative Scalar Field Coupled to Gravity

TL;DR

This paper introduces a model for a noncommutative scalar field coupled to gravity, demonstrating compatible solutions with cosmological symmetry and showing negligible effects during inflation.

Contribution

It extends the Moyal product to include gravity and analyzes solutions in a cosmological setting, highlighting the minimal impact of noncommutativity during inflation.

Findings

Solutions compatible with homogeneity and isotropy

Noncommutativity has negligible impact during slow-roll inflation

Model extends noncommutative scalar fields to gravitational contexts

Abstract

A model for a noncommutative scalar field coupled to gravity is proposed via an extension of the Moyal product. It is shown that there are solutions compatible with homogeneity and isotropy to first non-trivial order in the perturbation of the star-product, with the gravity sector described by a flat Robertson-Walker metric. We show that in the slow-roll regime of a typical chaotic inflationary scenario, noncommutativity has negligible impact.