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, $m_g<3.5\times {10}^{-20}\mathrm{eV}/{\mathrm{c}}^2$ (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 $m_g<5.2\times {10}^{-21}\mathrm{eV}/{\mathrm{c}}^2$ (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.

Figure 1

Eccentricity functions $F(e)$ and $G(e)$, defined in Eqs. (11) and (15), respectively.

Figure 2

The posterior distributions with two different priors for $m_g$.