Photon and Graviton Mass Limits

TL;DR

This work surveys the status of rest-mass limits for the photon and graviton, tracing a historical arc from inverse-square tests to gauge-invariant mass formalisms and Higgs/Stueckelberg constructions. It outlines theoretical frameworks (Proca, Stueckelberg, Abelian Higgs, Vainshtein, DGP) and compiles a spectrum of empirical constraints from local experiments, solar-system probes, and cosmic-scale observations, highlighting Yukawa-like deviations and the role of long-range fields. It discusses the interplay between dark matter and modified gravity in explaining galactic dynamics and cosmic acceleration, and it assesses the viability of mass-like effects for gravity in light of the vDVZ discontinuity, nonlinear screening, and higher-dimensional models. The paper concludes that photon-mass limits are now dominated by static-field and astronomical measurements, while graviton-mass questions remain tightly constrained but unresolved in the context of dark energy and large-scale structure, with future data likely to sharpen the bounds or reveal new physics.

Abstract

Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time.Historically, these studies have passed through three stages: (1) Testing the power in the inverse-square laws of Newton and Coulomb, (2) Seeking a nonzero value for the rest mass of photon or graviton, (3) Considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since our previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. "Cold dark matter" (slow, invisible classical particles) fits well at large scales. "Modified Newtonian dynamics" provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. "Dark energy" {\it might} be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. We summarize significant mass limits in a table.