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It seems that gravitational waves and gamma waves travail at about the same speed, arriving within seconds of each other over distances in the ranges of $10^6$LY. Naively, I would assume this caps the index of refraction (for gamma waves in intergalactic space) to something like $1+10^{-13}$. However I expect I'm making rather a lot of unfounded assumptions and probably missing a number of other things.

Has anyone actually worked through the physics and math to get a good answer to that question? What about the related question for different wavelengths or other, more dense, locations like interstellar space?

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