Could a Variable Speed of Light Theory Challenge the FLRW Metric in Cosmology?

[anorlunda]

Suppose we postulate that instead of the universe expanding, the speed of light was decreasing? Now we try to derive the Friedmann–Lemaître–Robertson–Walker (FLRW) metric from Newtonian conservation of energy. Would we get the same result?

 

[mfb]

You would need some way to contract gravitationally bound objects at the same time, otherwise we could measure this slowed speed of light.
And if you do that, you just redefine the length of a meter. This is possible, of course, but you get nothing new. I don't see how you plan to use Newtonian conservation of energy.

 

[Chronos]

Variable speed of light theories are plagued by a number of issues. It does not play well with any number of theories that incorporate c in their formulation - like the nuclear fine structure constant. It unavoidably breaks Lorentz, diffeomorphism and time translational invariance, implying a violation of energy conservation. And plays strangely with gravity, suggesting both gravity and its propogation speed must also vary to avoid conflicts with well established observational evidence. It's not that such a thing is not possible, but, would have far reaching consequences for GR and much of physics.