Graviton Mass and Memory

TL;DR

This paper investigates how a nonzero graviton mass affects gravitational memory, revealing that the effect diminishes with mass and distance, and proposing that observations of memory could constrain or rule out graviton mass.

Contribution

It provides a detailed calculation of gravitational memory in massive gravity, showing deviations from general relativity and exploring the impact of higher curvature terms.

Findings

Memory is reduced by a numerical factor in massive gravity, even in the massless limit.

For current bounds on graviton mass, memory is negligible beyond certain distances.

Higher curvature terms further decrease the gravitational memory effect.

Abstract

Gravitational memory, a residual change, arises after a finite gravitational wave pulse interacts with free masses. We calculate the memory effect in massive gravity as a function of the graviton mass $(m_g)$ and show that it is discretely different from the result of general relativity: the memory is reduced not just via the usual expected Yukawa decay but by a numerical factor which survives even in the massless limit. For the strongest existing bounds on the graviton mass, the memory is essentially wiped out for the sources located at distances above 10 Mpc. On the other hand, for the weaker bounds found in the LIGO observations, the memory is reduced to zero for distances above 0.1 Pc. Hence, we suggest that careful observations of the gravitational wave memory effect can rule out the graviton mass or significantly bound it. We also show that adding higher curvature terms reduces the memory effect.