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At the limit of weak static fields, general relativity becomes Newtonian gravity with a potential field that falls off as inverse distance rather than a theory of Yukawa-type fields with a finite range. General relativity also predicts that the speed of disturbances of its waves is c, the vacuum light speed, and is non-dispersive. For these reasons, the graviton, the boson for general relativity, can be considered to be massless. Massive gravitons, however, are features of some alternatives to general relativity. This has motivated experiments and observations that, so far, have been consistent with the zero-mass graviton of general relativity, but further tests will be valuable. A basis for new tests may be the high sensitivity gravitational wave (GW) experiments that are now being performed and the higher sensitivity experiments that are being planned. In these experiments, it should be feasible to detect low levels of dispersion due to non-zero graviton mass. One of the most promising techniques for such a detection may be the pulsar timing program that is sensitive to nano-Hertz GWs. Here, we present some details of such a detection scheme. The pulsar timing response to a GW background with the massive graviton is calculated, and the algorithm to detect the massive graviton is presented. We conclude that, with 90% probability, massless gravitons can be distinguished from gravitons heavier than 3 × 10-22 eV (Compton wavelength λg = 4.1 × 1012 km), if bi-weekly observation of 60 pulsars is performed for 5 years with a pulsar rms timing accuracy of 100 ns. If 60 pulsars are observed for 10 years with the same accuracy, the detectible graviton mass is reduced to 5 × 10-23 eV (λg = 2.5 × 1013 km); for 5 year observations of 100 or 300 pulsars, the sensitivity is respectively 2.5 × 10-22 (λg = 5.0 × 1012 km) and 10-22 eV (λg = 1.2 × 1013 km). Finally, a 10 year observation of 300 pulsars with 100 ns timing accuracy would probe graviton masses down to 3 × 10-23 eV (λ g = 4.1 × 1013 km). © 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.


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