Constraining the Noncommutative Spectral Action via Astrophysical Observations

TL;DR

This paper uses pulsar timing observations to place constraints on the gravitational sector of the noncommutative spectral action, linking astrophysical data to fundamental geometric models of particle physics and gravity.

Contribution

It provides the first astrophysical constraints on the noncommutative spectral action, connecting observational data with a potential grand unified theory.

Findings

Bounds on coupling constants are comparable to existing deviations from General Relativity.

Constraints are weak but consistent with current limits.

Future observations could tighten these bounds.

Abstract

The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. Thus, noncommutative geometry provides a geometric interpretation of particle physics coupled to curvature. In this letter we use observations of pulsar timings, assuming that no deviation from General Relativity has been observed, to constrain the gravitational sector of this theory. Thus, we directly constrain noncommutative geometry, a potential grand unified theory of physics, via astrophysical observations. Whilst the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from General Relativity in other settings and are likely to be further constrained by future observations.