Constraints on NonCommutative Spectral Action from Gravity Probe B and Torsion Balance Experiments

TL;DR

This paper constrains a parameter in noncommutative spectral geometry by analyzing weak gravitational fields with experimental data, setting bounds from Gravity Probe B and torsion balance experiments that surpass previous limits.

Contribution

It provides the first experimental bounds on the Weyl term parameter in noncommutative spectral geometry using gravitational experiments.

Findings

Gravity Probe B data sets a lower bound of $eta vert ext{gtrsim} 10^{-6}$m$^{-1}$.

Torsion balance experiments improve the bound to $eta vert ext{gtrsim} 10^{4}$m$^{-1}$.

The bounds are stronger than previous constraints on curvature squared terms.

Abstract

Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the gravitational, the electroweak and the strong forces are all described as purely gravitational forces on a unified noncommutative space-time. In this study, we infer a constraint on one of the three free parameters of the model, namely the one characterising the coupling constants at unification, by linearising the field equations in the limit of weak gravitational fields generated by a rotating gravitational source, and by making use of recent experimental data. In particular, using data obtained by Gravity Probe B, we set a lower bound on the Weyl term appearing in the noncommutative spectral action, namely $\beta \gtrsim 10^{-6}$m$^{-1}$. This constraint becomes stronger once we use results from torsion balance experiments, leading to $\beta \gtrsim 10^{4}$m$^{-1}$. The latter is much stronger than any constraint imposed so far to curvature squared terms.