my question is whether any new understanding can be gained by equating this increasing-mass explanation to the old expansion theory, if they both provide accurate representations of our observations

Deacon, it does not seem to have much potential to increase our understanding. The model just describes the SAME UNIVERSE but with different coordinates and units, so that the sizes of atoms shrink.

It may have some usefulness by teaching us to be more aware that you can have different mathematical descriptions of the same thing.

==quote Christoph Wetterich==
Our model should be interpreted as a new complementary picture of cosmology, not as opposing the more standard picture of an expanding universe. The different pictures are equivalent, describing the same physics. This can be seen by a redefinition of the metric, which leads to the “Einstein frame” with constant Planck mass and particle masses and an expanding universe. In the Einstein frame the big bang has a singularity, however. The possibility of different choices of fields describing the same reality may be called “field relativity”, in analogy to general relativity for the choice of different coordinate systems. Field relativity underlies the finding that strikingly different pictures, as an expanding or a shrinking universe, can describe the same reality.
==endquote==

So I would say, my non-expert impression is, that this does not open the door to any new physics or discovery in cosmology, but it can encourage greater sophistication in people's understanding of the relation of mathematics to reality. The two things shouldn't be confused. the description in a certain language must be carefully distinguished from the thing or process itself.

Wetterich (born 1952) is an outstanding senior theorist with important contributions going back at least to the 1990s if I recall correctly. He is in part responsible for the current interest in Asymptotic safety quantum gravity, and in a minimalist extension of Standard Particle Model, and for a successful prediction of ~125 Gev Higgs mass, before it was discovered. You may know all this about him but I wanted to say it out of respect in case someone doesn't. It still does not mean that this specific paper of his is important, though.

If I understand it correctly (most likely I don't) the model is not general relativistic. The Lagrangian and hence the equations are different. It starts with an effective action, which should include the quantum effects. My question is: is this a consequence of some quantum theory or is it only expected to be?

I think Marcus 'nailed it' in his reply. I sure don't know all the math, nor all observational evidence, but I find the author's statement

really surprising....astonishing

How can changing Planck, atom and electron mass each comport with ALL observations. Surely there is a chink in all this from observational cosmology?? Would it change theoretical estimates of early helium and hydrogen lithium, for example??

Marcus:

This is in keeping with Wetterich's own comment.

It reminds me of the various coordinate based descriptions of black holes which provide complementary perspectives, sometimes difficult to reconcile with each other. When first reading 'results' from BH models some stuff was really confounding for me. You really have to understand the coordinate limitations, solution approximations, underlying the math.

For example the Schwarzschild spacetime for BH is a solution to the vacuum EFE everywhere [no exterior mass]; Schwarzschild coordinates include a flat asymptotic spacetime [also not realistic]; An eternal black hole as described by SC geometry almost certainly does not exist in our universe; The Schwarzschild spacetime is static.....and likewise other results, like Kerr, also have infirmities. Yet they have revealed much.

On a more hopeful note, even Einstein did not recognize aspects of his own work, missing the melding/morphing of space and time until Minkowski made it explicit; maybe Wetterich has not yet realized some great insight to become available from his paper??

I see in the paper where this claim is made and if true could be quite extra ordinary. This condition is NOT an inherent part of the FLRW cosmological model; inflation is a 'patched in add on' to account for observations.

On the other hand, it also sounds like maybe this approach has a 'zero' starting point for Planck's constant...since planck mass grows over time.....hence no Heisenberg uncertainty....but that is not what seems to be claimed...

end of page 2.....I don't recognize that action expression [no surprise] but if the author starts from conventional models, then I guess everything is 'just another perspective'.

I can't sort out these apparent contradictions and post them here for consideration....

If it didn't expand from its initial high density state? Ohhhhh yeah.... LOTS of high energy radiation. So high that high mass particle-antiparticle pairs are created and annihilated constantly and no objects larger than fundamental particles can exist.