Variable Speed of Light Theories

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Yes, tons of it. They have even filmed light moving about at those speeds. It involves some pretty cool tech:

I don’t see why you would think it is unlikely. Both light and gravitational waves lack mass and are propagating through the same spacetime, so I would expect them to travel at the same speed.

Edited to add:

There is a pretty cool experiment that anyone can do using a chocolate bar and a microwave. You can get a rough measure of the speed of light at home:

http://www.planet-science.com/categories/over-11s/physics-is-fun!/2012/01/measure-the-speed-of-light-using-chocolate.aspx

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