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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.
In Einsteins general relativity, gravity is mediated by a massless spin-2 metric field, and its extension to include a mass for the graviton has profound implication for gravitation and cosmology. In 2002, Finn and Sutton used the gravitational-wave
The superradiant instability of black hole space-times has been used to place limits on ultra-light bosonic particles. We show that these limits are model dependent. While the initial growth of the mode is gravitational and thus model independent, th
Recent literature has shown that photon-photon forward scattering mediated by Euler-Heisenberg interactions may generate some amount of the circular polarization ($V$ modes) in the cosmic microwave background (CMB) photons. However, there is an appar
We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam
Rapidly rotating black holes are known to develop instabilities in the presence of a sufficiently light boson, a process which becomes efficient when the bosons Compton wavelength is roughly the size of the black hole. This phenomenon, known as black