Magueijo proposed that to solve one of the biggest physics problems, called the “horizon problem,” we might have to challenge the idea that the speed of light is constant. The problem states that the universe reached a uniform temperature long before energy-carrying photons traveling at constant speed could have had the time to reach all corners of the expanding universe.

The most accepted explanation for the horizon problem is something called inflation. It suggests that, after the Big Bang, the temperature evened out before the universe went through a rapid phase of expansion. But the inflation theory doesn’t sit well with many physicists, mainly because nobody can explain why inflation started and why it stopped.

Magueijo’s search for an alternative explanation is what made him question the speed of light. While it’s tempting to ditch a cornerstone of physics to solve other problems, it’s not wise to do so without setting out a testable hypothesis. That is why, until now, Magueijo’s hypothesis remained on the fringes of physics.

They propose that, at the very beginning of the universe, light and gravity traveled at different speeds. If photons moved faster than gravity, it would have given them enough time to travel to all parts of the universe and thus help reach temperature equilibrium.

Other physicists can test the hypothesis by measuring something called cosmic microwave background (CMB) radiation, which is a fossilized impression of the early universe that we can measure even today. The hypothesis suggests that the CMB should reflect the change in the speed of light and the speed of gravity as the temperature of the universe changed.

http://qz.com/846498/the-speed-of-light-is-constant-physicists-plan-to-test-a-new-theory-that-questions-einsteins-assumptions/

This appears to be relevant to Cosmology, or vice-versa.

Hi
Thanks for your post. Yes this is relevant to cosmology. At this point the best measurement of the claimed very precise prediction by the varying speed of light hypothesis is consistent with the world's best constraints coming from the Planck data analysis.
I am personally a bit sceptic regarding the claimed uniqueness of this prediction given that we know so little about the detailed physics at this epoch. If it is true the ever precise measurements coming from the Cosmic Microwave Background polarization and other probes will eventually be able to distinguish this model from other approaches that predict a range of possible values. If you're interested to know how this works (even if the data agrees with both models) ask me and I will tell you about relative model probabilities in Bayesian stats...

Till then,
All the best,
Ben

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Creator of Cosmology@Home