Limits on the speed of gravitational waves from pulsar timing

In this work, analyzing the propagation of electromagnetic waves in the field of gravitational waves, we show the presence and significance of the so-called surfing effect for pulsar timing measurements. It is shown that, due to the transverse nature of gravitational waves, the surfing effect leads to enormous pulsar timing residuals if the speed of gravitational waves is smaller than the speed of light. This fact allows one to place significant constraints on parameter epsilon, which characterizes the relative deviation of the speed of gravitational waves from the speed of light. We show that the existing constraints from pulsar timing measurements already place stringent limits on epsilon and consequently on the mass of the graviton m(g). The limits on m(g) less than or similar to 8.5 x 10(-24) are 2 orders of magnitude stronger than the current constraints from Solar System tests. The current constraints also allow one to rule out massive gravitons as possible candidates for cold dark matter in the galactic halo. In the near future, the gravitational wave background from extragalactic super massive black hole binaries, along with the expected submicrosecond pulsar timing accuracy, will allow one to achieve constraints of epsilon less than or similar to 0.4% and possibly stronger.