Bounding the mass of graviton in a dynamic regime with binary pulsars
In Einstein's general relativity, gravity is mediated by a massless spin-2 metric field, and its extension to include a mass for the graviton has profound implications for gravitation and cosmology. In 2002, Finn and Sutton [1] used the gravitational-wave (GW) backreaction in binary pulsars, and provided the first bound on the mass of graviton. Here we provide an improved analysis using nine well-timed binary pulsars with a phenomenological treatment. First, individual mass bounds from each pulsar are obtained in the frequentist approach with the help of an ordering principle. The best upper limit on the graviton mass, ${m}_{g}l3.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }\mathrm{eV}/{\mathrm{c}}^{2}$ (90% C.L.), comes from the Hulse-Taylor pulsar PSR $\mathrm{B}1913+16$. Then, we combine individual pulsars using the Bayesian theorem, and get ${m}_{g}l5.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\text{ }\text{ }\mathrm{eV}/{\mathrm{c}}^{2}$ (90% C.L.) with a uniform prior for $\mathrm{ln}\text{ }{m}_{g}$. This limit improves the Finn-Sutton limit by a factor of more than 10. Though it is not as tight as those from GWs and the Solar System, it provides an independent and complementary bound from a dynamic regime.