# What is the upper bound for the index of refraction of space?

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?