Bounding the Mass of the Graviton

We studied the possibility of placing a bound on the mass of the graviton using gravitational-wave data from inspiralling compact binaries (Will 1998). The potential bounds were refined by incorporating better LISA noise curves, the effects of spins and the contributions of higher harmonics in the waveforms [see Will and Yunes (2004), Berti, Buonanno and Will (2005a,2005b), Arun and Will (2009), Stavridis and Will (2009)]. This idea came to fruition in 2015 with the first detection of gravitational waves by LIGO, where they placed a lower bound of 1.6 x 10^13 km on the graviton Compton wavelength.

Meanwhile, dramatic improvements in solar-system orbital data have made it possible to place a competitive bound on the graviton mass by testing the effects of the resulting Yukawa-type modification of the Newtonian gravitational potential. By examining published uncertainties on the perihelion advances on Mercury, Mars and Jupiter, we (Will 2018) estimated a bound of between 1.2 and 2.2 x 10^14 km. However Bernus and colleagues pointed out that, if one modifies Newtonian gravity with such a Yukawa factor, then estimates of many solar system parameters (masses, orbital parameters, etc) are affected, with multiple correlations among them, and therefore using "post-fit" uncertainties may give a misleading results. They carried out a complete reanalysis of all solar-system data using the INPOP ephemeris code (Bernus et al. 2019, 2020) placed a weaker but more reliable bound of 3.4 x 10^13 km.

Analysing a catalogue of gravitational wave events obtained up to late 2019, the LIGO-Virgo collaboration placed a combined bound of 10^13 km. (LIGO 2020)

A new general relativistic contribution to Mercury's perihelion advance

We pointed out the existence of a new general relativistic contribution to the perihelion advance of Mercury that, while smaller than the contributions arising from the solar quadrupole moment and angular momentum, is 100 times larger than the second-post-Newtonian contribution (Will 2018). It arises in part from relativistic ``cross-terms'' in the post-Newtonian equations of motion between Mercury's interaction with the Sun and with the other planets, and in part from an interaction between Mercury's motion and the gravitomagnetic field of the moving planets. At a few parts in 10^6 of the leading general relativistic precession of 42.98 arcseconds per century, these effects are likely to be detectable by the BepiColombo mission to place and track two orbiters around Mercury, scheduled for launch around 2018.

Testing general relativity with compact-body orbits: A modified Einstein-Infeld-Hoffmann framework

We described a general framework for analyzing orbits of systems containing compact objects in a class of Lagrangian-based alternative theories of gravity that also admit a global preferred reference frame (Will 2018). The framework is based on a modified Einstein-Infeld-Hoffmann (EIH) formalism that uses a post-Newtonian N-body Lagrangian with arbitrary parameters that depend on the theory of gravity and on ``sensitivities'' that encode the effects of the bodies' internal structure on their motion. We determined the modified EIH parameters for the Einstein-Aether and Khronometric vector-tensor theories of gravity. We obtained the effects of motion relative to a preferred universal frame on the orbital parameters of binary systems containing neutron stars, such as a class of ultra-circular pulsar-white dwarf binaries; the amplitudes of the effects depend upon ``strong-field'' preferred-frame parameters which we related to the fundamental modified EIH parameters.

Review Articles on Tests of GR

Articles by Clifford Will:

The Confrontation between General Relativity and Experiment (here)

Was Einstein right? A centenary assessment (here)

The 1919 measurement of the deflection of light (here)


Other Review articles:

  • Ingrid Stairs on Binary Pulsars (here)
  • David Mattingly on tests of Lorentz Invariance(here)
  • Jean-Phillippe Uzan on Varying Constants (here)
  • Dimitrios Psaltis on Strong-Field tests of GR (here)
  • Neil Ashby on Relativity in GPS (here)
  • Benoît Famaey and Stacy McGaugh on MOND (here)
  • Claudia de Rham on Massive Gravity (here)
  • Nicolás Yunes and Xavier Siemens on Gravitational-Wave tests of GR (ground based and pulsar timing) (here)
  • Jonathan Gair et al on Gravitational-Wave tests of GR (space based) (here)
  • Stephen Merkowitz on Lunar laser ranging tests of GR (here)
  • Slava Turyshev and Viktor Toth on the Pioneer Anomaly (here)
  • Antonio De Felice and Shinji Tsujikawa on f(R) theories (here)


Projects Page | Clifford Will's Home Page | Physics Department | University of Florida