[Filligree]

I'm with the first one, then. I consider the Kolomogorov complexity of the laws of physics to be important, and initial conditions to be part of said laws, but I don't think it adds much complexity to posit that the initial conditions are very, very simple (and thus low-entropy).

[raattgift]

Taking that position also gives you the answer to why we won't see black holes fissioning into outspiralling pairs of neutron stars, or shards of glass spontaneously reassembling into a wineglass that leaps off the floor into someone's hand. The only cost is extremely exquisitely finely placed stress-energy-momentum in the early universe into the infinite past.

If you have no problem with an infinite history of ever lower entropy, then luckily observations to date do not contradict this sort of cosmology, and under time-reversal the "movie" showing the universe crunching into an ever more orderly state forever isn't very shocking other than we arrange our lives with the movie playing the other way, sweeping up broken shards of glass rather than catching rising stemware. Maybe conscious life somewhere else in our Hubble volume arranges their lives in that way, though, unbreaking and unmaking their artefacts and thinking our way of doing things is strange.

Some other questions for you: how far does this cosmology's future grow? Do we get infinite entropy in the infinite future? If we don't have an infinite future, why do we have an infinite ever-more-orderly past? If we have an infinite future, do you suppress fluctuations? Do you wholly suppress Poincaré recurrence? How would you distinguish us here as us here now from a recurrence? Are we a recurrence? etc.

These questions do not seem as amenable to testing with current technology as questions arising from other cosmologies.

[Filligree]

Well, let's see. I don't have much time to spend on this, and I'm well aware that I'm an amateur anyway, but...

One point, at least. I see no reason why a theory being difficult to test should count even slightly against the probability of its being true. Sure, it's inconvenient -- and there's something to be said for focusing on ideas that can be tested -- but since when was nature ever constrained to convenience?

As to your other questions...

I'm not sure where the 'infinite past' comes from. There's a single slice of space-time that needs to be constrained; everything else can flow from there, in both directions. If it's a low-entropy constraint then causality would naturally flow away from that slice. The two sides should be mirrors of each other, though.

As to the far future... that's harder.

- My intuition is that, when you're trying to guess at which of many possible universes you actually live in, the amount of "runtime" the theoretical universe spends on computing you (that is, some form of life, at least) should matter. But that's problematic, since it seems to predict higher complexity of the physical laws in exchange for a universe that's denser with life, and it's not what we see.

- More realistically, perhaps, the big rip might be a thing. Recurrence could fail to happen because the far future doesn't allow for structures complex enough to have thoughts, not even by random chance.

I prefer to punt on the question, though. I don't know enough to have an informed opinion.