Gravitational Waves in the Spectral Action of Noncommutative Geometry

TL;DR

This paper explores how noncommutative geometry modifies Einstein's gravity, leading to a massive graviton mode that significantly impacts gravitational wave production and energy loss in binary systems.

Contribution

It derives the weak field limit of a noncommutative geometric gravitational theory and analyzes the resulting modifications to gravitational wave dynamics and energy emission.

Findings

Presence of a massive graviton mode alters gravitational wave energy loss.

Modified energy loss formula for binary systems with quadrupole moments.

Significant changes in gravitational wave propagation due to noncommutative geometry.

Abstract

The spectral triple approach to noncommutative geometry allows one to develop the entire standard model (and supersymmetric extensions) of particle physics from a purely geometry stand point and thus treats both gravity and particle physics on the same footing. The bosonic sector of the theory contains a modification to Einstein-Hilbert gravity, involving a nonconformal coupling of curvature to the Higgs field and conformal Weyl term (in addition to a nondynamical topological term). In this paper we derive the weak field limit of this gravitational theory and show that the production and dynamics of gravitational waves are significantly altered. In particular, we show that the graviton contains a massive mode that alters the energy lost to gravitational radiation, in systems with evolving quadrupole moment. We explicitly calculate the general solution and apply it to systems with periodically varying quadrupole moments, focusing in particular on the the well know energy loss formula for circular binaries.