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, m₆<3. 510^-20 eV/c^2 (90% C. L. ), comes from the Hulse-Taylor pulsar PSR B1913+16. Then, we combine individual pulsars using the Bayesian theorem, and get m₆<5. 210^-21 eV/c^2 (90% C. L. ) with a uniform prior for ln m₆. 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.