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 implication for gravitation and cosmology. In 2002, Finn and Sutton used the gravitational-wave (GW) back-reaction in binary pulsars, and provided the first bound on the mass of graviton. Here we provide an improved analysis using 9 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, $m_{g}<3.5\times10^{-20} \, {\rm eV}/c^{2}$ (90% C.L.), comes from the Hulse-Taylor pulsar PSR B1913+16. Then, we combine individual pulsars using the Bayesian theorem, and get $m_{g}<5.2\times10^{-21} \, {\rm eV}/c^{2}$ (90% C.L.) with a uniform prior for $\ln m_g$. 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.