Physicists Elias Kiritsis and Stephon Alexander independently developed variable speed of light (VSL) models that could be incorporated into string theory, and Alexander later worked with Magueijo on refining these concepts (even though Magueijo is critical of string theory’s lack of contact with experiment).
In two separate efforts, physicists have developed a system where the speed of light actually would not be constant, as a means of explaining the horizon problem without the need of inflation. The earliest system of the variable speed of light (VSL) was proposed by John Moffat (who later incorporated the idea into his modified gravity theory), and a later system was developed by João Magueijo and Andreas Albrecht.
The horizon problem is based on the idea that distant regions of the universe couldn’t communicate their temperatures because they are so far apart light hasn’t had time to get from one to the other. The solution proposed by inflation theory is that the regions were once much closer together, so they could communicate.
In VSL theories, another alternative is proposed: The two regions could communicate because light traveled faster in the past than it does now.
Moffat proposed his VSL model in 1992, allowing for the speed of light in the early universe to be very large — about 100,000 trillion trillion times the current values. This would allow for all regions of the observable universe to easily communicate with each other.
To get this to work out, Moffat had to make a conjecture that the Lorentz invariance — the basic symmetry of special relativity — was somehow spontaneously broken in the early universe. Moffat’s prediction results in a period of rapid heat transfer throughout the universe that results in the same effects as an inflationary model.
In 1998, physicist João Magueijo came up with a similar theory, in collaboration with Aldreas Albrecht. Their approach, developed without any knowledge of Moffat’s work, was very similar — which they acknowledged upon learning of it.
This work was published a bit more prominently than Moffat’s (largely because they were more stubborn about pursuing publication in the prestigious Physical Review D, which had rejected Moffat’s earlier paper). This later work has inspired others, such as Cambridge physicist John Barrow, to begin investigating this idea.
One piece of support for VSL approaches is that recent research by John Webb and others has indicated that the fine-structure constant may not have always been constant. The fine-structure constant is a ratio made up from Planck’s constant, the charge on the electron, and the speed of light. It’s a value that shows up in some physical equations.
If the fine-structure constant has changed over time, then at least one of these values (and possibly more than one) has also been changing.
The spectral lines emitted by atoms are defined by Planck’s constant. Scientists know from observations that these spectral lines haven’t changed, so it’s unlikely that Planck’s constant has changed. (Thanks to John Moffat for clearing that up.) Still, any change in the fine-structure constant could be explained by varying either the speed of light or the electron charge (or both).
These proposals are intriguing, but the physics community in general remains committed to the inflation model. Both VSL and inflation require some strange behavior in the early moments of the universe, but it’s unclear that inflation is inherently more realistic than VSL. It’s possible that further evidence of varying constants will ultimately lead to support of VSL over inflation, but that day seems a long way off, if it ever happens.