Bounds on the photon mass via the Shapiro effect in the solar system

Abstract

We study the effects of a finite mass for the photon on its propagation in a weak gravitational field. In particular, we analyse the gravitational time delay, also known as the Shapiro effect. We work in isotropic coordinates in the weak-field limit and find that the mass-dependent corrections enhance the gravitational time delay. Doppler-tracking data from the Cassini mission allow us to set an upper bound on the photon mass, namely $m_{\gamma }<4.9\times 10^{-7}eV/{\mathrm{c}}^2$ at $95\%$ CL. We also discuss next-generation solar-system tests of general relativity that could improve this upper limit, potentially by a factor of ten. Though not competitive with the currently best limits, our bound is at the ballpark of earlier ones based on the gravitational bending of light by the Sun.

12 pages, 3 figures. Added appendix D. Matches published version

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