Remarks on Graviton Propagation in Light of GW 150914

The observation of gravitational waves from the Laser Interferometer Gravitational-Wave Observatory (LIGO) event GW150914 may be used to constrain the possibility of Lorentz violation in graviton propagation, and the observation by the Fermi Gamma-Ray Burst Monitor of a transient source in apparent coincidence may be used to constrain the difference between the velocities of light and gravitational waves: cg − cγ < 10−17. February 2016 ar X iv :1 60 2. 04 76 4v 2 [ gr -q c] 1 6 Ju n 20 16 The discovery of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) in event GW150914 [1] opens a new era in astronomy, making possible the measurement of astrophysical processes that have been inaccessible to observations with electromagnetic waves. The question then arises what fundamental physics we can learn from gravitational wave observations in general and LIGO event GW150914 in particular. As examples, the LIGO Collaboration itself [2] has reported an upper limit on the graviton mass mg < 10 −22 eV, and it has been suggested that observations of binary black-hole mergers could constrain models of quantum physics near black-hole event horizons [3]. In this comment we derive two additional constraints on graviton propagation, assuming that it is massless. First, the LIGO data on GW150914 can be used to constrain the possibility of Lorentz violation [4] in gravitational wave propagation, assuming that low-frequency gravitational waves (low-energy gravitons) travel at the conventional speed of light in vacuo c (that we set to unity from now on), whereas higher-frequency waves (higher-energy gravitons) may travel at frequency(energy-)dependent velocities. Secondly, assuming instead that the velocities of gravitational and electromagnetic waves cg and cγ are frequency(energy-)independent, we use the apparent coincidence of a transient source with photon energies > 50 keV observed by the Fermi Gamma-Ray Burst Monitor (GBM) [5] to constrain the difference between the velocities of light and gravitational waves in vacuo: cγ − cg < 10−17c. The LIGO constraint on the graviton mass was obtained from a detailed numerical comparison of the measured GW150914 wave-form with that calculated for a black-hole merger [2]. We recall that the GW150914 signal consisted of a ‘chirp’ of increasing frequencies ω ∼ 100 Hz, with a range of frequencies ∆ω = O(100) Hz. The presence of a gravitino mass would induce an energy(frequency-)dependent deviation of the velocities of the waves emitted during the ‘chirp’ from that of light: ∆v|mg ' −mg/2ω. Such a deviation ∆v would cause a dispersion in their arrival times [6], which is constrained by concordance of the observed signal with numerical relativity calculations. It was suggested in [7] that quantum-gravitational effects might induce an energy(frequency-)dependent velocity of propagation in vacuo for both electromagnetic and gravitational waves ∆v|LV n ' −ξ(ω/Mn) : n = 1 or 2 where Mn is some large mass scale, where ξ = +1(−1) for subluminal (superluminal) propagation and low-energy (-frequency) waves would travel at the conventional velocity of light. Such a Lorentzviolating effect would give rise to an energy-dependent dispersion in the arrival times of gravitational waves, though with a different energy dependence from a graviton mass. Such Lorentz violation might be induced by the effects of space-time foam on wave prop-