The article didn't really explain why expanding universe is in any kind of a conflict with unitary. The fact that a randomly added photon would become a black hole in the past isn't convincing since one can't just add a particle out of nowhere.
I think that’s the gist actually. Unitarity does seem to raise problems in the cosmos (information loss) but naively violating it by adding a photon gets you this ridiculous paradox of black holes turning into photons. So if you’re going to relax the unitarity assumption, you have to do it carefully. I guess this is their program with isometry.
It probes the question, "is the theory stable under small perturbation?", which is almost always a good question.
Stability here means that the effects of introducing a small perturbation are proportional to the perturbation itself. Unitarity implies this kind of stability.
Perturbation theory has been an important tool in physics for hundreds of years <https://en.wikipedia.org/wiki/Perturbation_theory#History>, and randomly adding a photon to a known universe and tracing out its effects is a perfectly reasonable application of it. It amounts to a "What if?" story but with mathematics and ideally some rigour. "What if we had a universe described by the Standard Model of Particle Physics, and the Standard Model of Cosmology, and introduced a single photon at various energies and at various times? How does that change the universe? Can we do better than just 'materialize' it out of thin air, by giving it some consistent back-story/history, no matter where we 'materialize' it and no matter what energy it has at that materialization point? Can we do all of the above within the constraints imposed by the two standard theories?"
In an expanding universe, the broad family of theories discussed in the article seem to be only semi-stable, breaking the world in one direction even given only a tiny perturbation. Small perturbations practically anywhere in the expanding universe all lead to small future effects, but under time reversal may lead to large past effects (or equivalently, our small perturbation can only have a consistent history if produced by an extreme event).
In the direction where the universe's matter gets ever thinner and colder, the small-perturturbation-photon ("spp") gets redder and redder, and might travel eternally without interacting without interacting with anything else. We can effectively guarantee that by introducing our spp in the extremely distant future, when there is less than one galaxy cluster per Hubble volume. Coupled to the expansion, the spp's wavelength grows to cosmological lengths and it traverses increasingly empty space, and for all we know it could continue to evolve that way eternally, growing ever redder (wavelength increasing) and with ever decreasing probability of interaction. Even if it were to interact with some other matter, the effect would be diminishingly tiny over time.
But in the opposite timelike direction, over time the probability of interacting with something else grows. It can't fly to the eternal past because there is dense structure in the past, so the probability of interaction increases. That interaction will be with the ever hotter gamma ray the backwards-in-time spp evolves into. Moreover that hot gamma ray can't grow ever bluer if there is a minimum wavelength. So we've already revealed some shortcomings in the "ultraviolet completion" of the Standard Model as long as the spp is introduced far enough into the big bang's future and allowed to travel back in time with the contraction (time-reversed expansion) of the universe.
We can also ask about whether an spp's earliest state and latest state are physically plausible.
The far future of our universe will have lots of very low frequency photons zipping through practically empty space; the spp is not physically different from them, and if we looked we could probably find a photon with a "natural" origin in the system that we perturbed with the spp such that the spp and the "natural" photon are indistinguishable. We can even start with a super-hot gamma ray photon as our spp and have a very good chance that it will simply cool down (gravitationally redden) in the future direction, eventually becoming just like other low-frequency photons. It barely matters where or when we "initially" introduce a forward-in-time-travelling gamma ray spp, so long as it has an unobstructed path to deepest space. So the spp's late times are perfectly plausible.
The early times however require us to take care in where we introduce the spp and how long its wavelength is "initially" (at the point where we introduce it). If it's very short wavelength then very soon before the "initial" introduction, the backwards-in-time travelling spp hits the wall in our understanding of the extremely-high-energy behaviour of the Standard Model. If the "initial" introduction is too far in the future then even a radio-frequency spp will blueshift so much that it will hit the wall. We don't see arbitrarily high-energy gamma rays in our sky, so our spp might be pretty easy to distinguish from any "mere" <https://en.wikipedia.org/wiki/Ultra-high-energy_gamma_ray> with produced naturally in the universe we are trying to negligibly perturb.
The article's line trying to summarize Giddings, "... its wavelength will eventually get impossibly small, concentrating its energy so greatly that the photon collapses into a black hole" captures the idea above, making an educated guess about the possibility of a minimum wavelength for a photon. But the point that wasn't captured is that a small perturbation doesn't raise any theoretical questions in one timelike direction, but very likely does in the other timelike direction. The feature associated with this "hey, did we break the entire theory by adding just a single low-energy particle?" is the expansion of space in one timelike direction / the contraction of space in the opposite timelike direction.
If we have a non-expanding space, then there will be no cosmological redshift, so our "initial" photon's wavelength is the same as its final wavelength, in both directions of time and out to eternity. The small perturbation photon's effects remain proportionately small everywhere and everywhen (rather than that being only the case practically everywhere in the future, and only in some places in the past).
