Hard problems

The headline says "Researchers Reveal How an Expanding Universe Can Emerge Without a “Big Bang”". The team figured a way of having an emergent expanding universe without a singularity. They start with a flat spacetime that is rotating, and small phase transitions can occur which act a little like expanding bubbles. OK, cool. But in the fine print:

In a first step, a spacetime with only two spatial dimensions was considered. “But there is no reason why the same should not be true for a universe with three spatial dimensions”, says Grumiller.

Our own universe does not seem to have come into existence this way. The phase-transition model is not meant to replace the theory of the Big Bang.

Or in other words, the model they show is a 2D+time model instead of the 3D+time world we live in. So you'd think that this is not a huge deal, call back when they get to 3 dimensions. Fair enough.

The linked article tries to explain why this is interesting--the short version is that there's been an influential theory that links quantum field theory to gravity in a "holographic" way. One example given to explain the conjecture was that if it were true, then a solution of the equations on the boundary would define everything inside; sort of like a hologram (2D) that reconstructs to something 3D. Which seems to kind of flatten us out a bit, but it isn't as bad as it sounds.

But: problems that are OK in 2D can be fiendishly hard in 3D. I've been fiddling with a little problem and wondered if hyperdeterminants would help (and if you understand that link on the first read-through you're doing better than I did). There is a closed form expression for the 2x2x2 tensor, but 3x3x3? To quote a paper from arxiv: "The classical case p = 1 is much easier than the case p>=2 mainly because there are only finitely many orbits for the action of GL(V0) x GL(V1)". (I'm calling this a dead end: using their notation I have p=2.)

Or the 2-body problem. The Earth and Moon, in isolation, form a very easy dynamical system; closed form solution, all is well. Including the effects of tides muddies it a lot. Add a third body and not only is there no closed form solution, the system may or may not be stable depending on small changes in the initial conditions--good old chaos.

So I'm not as sanguine about possible solutions as Dr. Grumiller. There are too many surprises.

Of course, once they have a solution, then they have to compare the predictions of that with what we actually see. This has been done (with resulting retuning) for the standard cosmological models, and it has taken many man-years to do the computations and comparisons. Even the unsatisfactory current theories satisfy a lot of constraints that a new model will also have to prove itself against. If we had the accurate Theory of Everything handed to us tomorrow morning, it would still take years--maybe even decades--before we could be sure that it was even as good as what we already have.