Yeah Wolram, I think that is a very interesting question. It is not one that I can answer in a complete or satisfactory way, but I can indicate some ideas that other people have.
...<gap of several hours>...
A social event intervened. I'm back at least for the moment now.
One of the thing that happened when they quantized the Einstein law of gravity in the simplest most straightforward way they could think of is that you get a law of gravity where the behavior depends very slightly on density due to quantum effects. So slightly that at ordinary density, or even the density at the core of a star, you don't notice---gravity still behaves in an almost classical way, as you would expect from Newton's law.
But at very very high density these quantum effects become predominant and gravity acts very different from its classic low-density behavior. At near-Planckian density the model says it actually pushes stuff apart rather than making it continue getting more and more compact.*
This is not something people especially wanted to have happen, or were expecting. As it happened in the particular case of Loop, they rewrote the classic (nonquantum) equations for the universe in a quantized form and then they programmed their computer to run those equations and simulate a collapsing universe, and lo and behold it bounced. The same thing had happened earlier when a young postdoc had approximated the evolution with a difference equation and run that on the computer---the approximate step by step evolutionary model bounced (that was Bojowald, around 2001 or so). There was a lot of arguing about this, and people challenging and proposing improvements and making the equations smoother and refined, and it kept bouncing. Then in 2005 they developed a more advanced model that everybody in the group thought was OK and programmed it as a heavy-duty computer sim, and it still bounced.
Apparently the basic reason is that the quantum world doesn't like to be completely determined and pinned down with absolute certainty. If you try to nail too much down into too small a space and be absolutely certain about where it is, then it fights back. This is a very sloppy oversimplified way of talking but that is what it looks like to me is going on.
We don't know if this model or that model is right. By now there are quantum cosmology models being invented and investigated by a number of people. It is time to derive predictions from them about features of the CMB that we can check, and so we can kill off some. But so far I don't know of any quantum cosmo model of a collapsing universe where the universe just collapses tamely down to a point. There is always something weird that happens. Not always the same. Sometimes the bounce goes haywire and a universe with fewer spatial dimensions comes out. Sorry. The computer simulations do not always give the same because they are trying different prior conditions.
Sometimes the bounce gets stuck in some weird state. Sometimes you get a kind of crippled universe. But surprisingly often it comes out pretty much as you might expect, a nice expanding world pretty much like ours.
So at this point people arent worrying about the question you asked----about how can this happen because isn't gravity so strong it would not allow a bounce to happen? Nobody worries about that any more. What they are worrying about is observational testing.
Each model must have its own almost imperceptible quirks and kinks, so that it produces a signature (distinct from any other model) which one can see written in the sky, in the CMB microwave temperature map.
If you were in this business, and had some graduate students and postdocs working for you, this is what you would be driving your team of people to investigate now. What peculiar signature in the sky map is going to result from a bounce conducted with each particular model? So we can tell which ones are most obviously wrong and throw them out.
This is the best I can do as a birdseye overview of things at the moment. I hope it makes sense.
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*surprisingly, this effect shows up both in Loop and in Martin Reuter's (asymptotic safe) approach. The two are technically very different. The technical detail is not the important thing. What matters is that regardless of your approach, quantizing gravity makes it behave markedly different at very high density.
