The Varying Speed of Light Cosmology
The varying speed of light cosmology has been proposed independently by Jean-Pierre Petit in 1988, John Moffat in 1992, and the two-man team of Andreas Albrecht and João Magueijo in 1998 to explain the horizon problem of cosmology and propose an alternative to cosmic inflation. An alternative VSL model has also been proposed.
In Petit's VSL model, the variation of c accompanies the joint variations of all physical constants combined to space and time scale factors changes, so that all equations and measurements of these constants remain unchanged through the evolution of the universe. The Einstein field equations remain invariant through convenient joint variations of c and G in Einstein's constant. Late-model restricts the variation of constants to the higher energy density of the early universe, at the very beginning of the Radiation-Dominated Era where spacetime is identified to space-entropy with a metric conformally flat. However it should be noted that while this was the first VSL model to be published, and the sole to date where an evolution law is given relating the joint variations of constants through time while leaving the physics unchanged, these papers received few citations in the later VSL literature.
The idea from Moffat and the team Albrecht-Magueijo is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions of the expanding universe have had time to interact at the beginning of the universe. There is no known way to solve the horizon problem with variation of the fine-structure constant, because its variation does not change the causal structure of spacetime. To do so would require modifying gravity by varying Newton's constant or redefining special relativity . Classically, varying speed of light cosmologies propose to circumvent this by varying the dimensionful quantity c by breaking the Lorentz invariance of Einstein's theories of general and special relativity in a particular way. More modern formulations preserve local Lorentz invariance.
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