In the standard effective field theory of gravity, gravitational waves on cosmological backgrounds propagate at a speed differing from unity, and analyticity arguments favor superluminal speed relative to matter.
It's Hard to Learn How Gravity and Electromagnetism Couple
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abstract
We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.
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The Speed of Gravity
In the standard effective field theory of gravity, gravitational waves on cosmological backgrounds propagate at a speed differing from unity, and analyticity arguments favor superluminal speed relative to matter.