Pulsar tests of the graviton mass

In Einstein's general relativity (GR), gravity is described by a massless spin-2 metric field, and the extension of GR to include a mass term for the graviton has profound implication for gravitation and cosmology. Besides the gravity experiments carried out in the Solar System and those recently with gravitational waves (GWs), pulsar timing observations provide a complementary means to test the masslessness of graviton. In this contribution, I overview three methods in probing the mass of graviton from precision timing of binary pulsars via the modified gravitational radiation (hence, the observed damping rate of the orbital period), as well as from the pulsar-timing-array (PTA) experiments via the modified Hellings-Downs angular-correlation curve. These tests probe different aspects of gravitation in its kinematics and dynamics, complementing tests of other kinds and providing valuable information to the fundamental theory of gravity.