[twawaaay]

> The key point though is that their mechanism cannot work in vacuum. It absolutely requires that the light travels significantly slower than the gravitational radiation

I am not a physicist, but I understand we are talking about Universe so early after Big Bang that it wasn't yet transparent to light. There simply wasn't vacuum yet if by vacuum you mean electromagnetic waves being able to travel long distances.

[raattgift]

I am not sure what you're getting at exactly. Although the paper does touch on early universe cosmology, the authors do their principal analysis using the refractive value for water, and there were no interstellar water clouds before early supernovae started generating oxygen. The authors also explicitly contemplate observables generated by LIGO-accessible compact binary mergers ("compact" here means black holes and neutron stars), all of which postdate the first stars.

In physical cosmology (and especially considering alternatives to General Relativity) it is very common to consider the possibility that some effect is strong in the very early universe and so weak as to be undetectable at present times (or even as early as the first galaxies or the surface of last scattering). Examples include auxiliary gravitational fields ("bimetric" theories, for example) that decay in the early universe, variable-speed-of-light/variable-Newton's-constant theories, and so forth.

Although one might think "hm, it's very convenient that an important effect only happens so early that we cannot use telescopes to see it", there is very good evidence for electroweak unification and cosmic inflation, both of which terminated (in different ways) in the very early universe, and are (or arguably were) too difficult to directly observe this late in the universe's history. Additionally there is ample indirect evidence that (if it exists) is within our reach.

That the hypothesized graviton-photon mechanism cannot work in vacuum makes it at least very difficult to test (or observe with telescopes) today, however the final section of the paper does suggest that if it happens in nature, where it happens is likely to become accessible to us in due course. This is not a theory that has a hard cut-off in the early universe; it is just a hypothesis that to be realized requires a configuration of e.g. binaries and molecular clouds that is not very close to what we commonly observe. (Double-binary compact objects in dusty environments might end up being commonplace though, and in those settings one could expect changes in "multimessenger" signals if the authors' ideas are correct. It's amazing how many star systems are turning out to be triples, and we know of triple-compact-star systems; there are a number of known quadruples like DI Chamaelontis; and Gamma Cassiopeiae is a system of at least seven ~stellar mass bodies.)

[twawaaay]

What you say doesn't make much sense.

AFAIK there exists no popular belief that physics was different in early universe. The physics was the same, the only thing that was different was physical conditions. Meaning everything was densely packed together.

If you, even for a moment, assume that laws were different in early universe then you essentially lost any possibility to predict anything.