What were the necessary conditions to allow a big bang to occur?
I don't know how the following analogy fits with the current models but is one I think has value.
Suppose I have a (solid) concrete slab 10' long held in place at both ends and I start putting weights in the center: 500 lbs, 100lbs, 50 lbs, . . . two pounds, half-pound. The slab doesn't bend (much). Eventually I reach the critical point this slab can support. Maybe even a feather more and it suddenly fails catastropically. :)
That is model-dependent. There are several models of conditions around the start of expansion. We don't yet have the means to test them: to rule some out and prefer others.
The answer to your question depends on which model you are working with.
The research field is called quantum cosmology. Classical cosmology (based on 1915 vintage General Relativity) does not apply at very high energies and densities, so it fails near the start of expansion and you need the quantum version. Books and research papers on this are coming out.
Currently the dominant model in QC is the type called Loop Quantum Cosmology (LQC). The way you can see this is to do a keyword listing of the recent research papers, ranked by how often they are cited. Almost all of the top 25 papers will turn out to be LQC.
So one way to answer your question is to say what conditions are required for bang to happen in the LQC model. That's easy.
In LQC they run computer models of the universe and they evolve continuously on back to before the start of expansion, showing a universe roughly similar to ours but collapsing. So the models give a kind of putative window on pre-bang.
In the model, when the density reaches a certain critical level, quantum gravity effects take over and, in effect, gravity repels instead of attracts. There is a bounce and expansion is given a huge kickoff. A certain limited amount of exponentially accelerating expansion (inflation) occurs naturally, without having to be put in by hand. More can be achieved by putting in an "inflaton" field like that used in other inflation scenarios, but you get a certain amount free.
The quantum gravity effect that causes the bounce was also not put in by hand. It simply turned up when the main classical (non-quantum) equation of cosmology was quantized. When they switched over to a quantum version, they found gravity attraction did not continue to get stronger at higher and higher density, but actually became repellent at extreme density. So that Planck density could not be reached, in gravitational collapse, but was replaced by a bounce.
In recent computer simulations the bounce seems to occur consistently at around 40 percent of Planck density. (This is an insanely high density, if you want to know it in metric units tell me but otherwise I won't even bother to write it down.)
All this does not mean that LQC is right. But it is in principle testable, by examining fine detail in the radiation from the early universe, and it is currently the dominant line of research in QC.
Here is a keyword search of recent (date > 2006) papers.
If you change the search to go back earlier (1989 < date < 1999) you will find String-inspired papers dominate the QC field, along with papers following an approach by Stephen Hawking which has now pretty much dropped out of sight. In between (1999 < date < 2006) there is a gradual transition to Loop. Let me know if you want some help with the Spires search tool. I think it's interesting to see how things have shifted.
Was the model you mentioned talking about in what condition the expanding stops and Big Crunch starts?
No, young kiwi. At this point they can only crank the model back a little farther and peer a little farther back in time (assuming the model is right and can be checked out using present observations.) For now, using a straightforward, conceptually economical, model that is already pretty good. But they sure are not answering any big questions like "where did it, why did it etc"
Keep asking though. Keep bugging them! (Good question.)
Is there any model talking about in what condition the expanding stops and Big Crunch starts?
Certainly, Youngkiwi, there is that. A key issue is dark energy, though. It isn't clear that DE is constant or that it is bound to be the same in a prior collapsing phase of the universe as it is here. In the extreme conditions of a bounce some stuff might be altered.
Because of the type of DE that we seem to have at this point, and assuming it is constant, our universe is destined to expand forever. If there was a bounce, and a prior contracting phase it has to have been different at least as regards the dark energy field.
At least IMHO, can't claim any expertise.
If only we could put DE out of the picture then there is a simple answer to your question. It's cut and dried. I have to go for now, but I'll be back and in the meantime someone else can step in. It's well known---the critical density. If the real observed density of matter and energy is bigger than the critical level then the U is destined to eventually stop expanding and to undergo collapse. Otherwise it keeps expanding. There is a nice simple pair of differential equations called the Friedman equations (see wikipedia) which predicts the course of expansion and contraction in that case. You may know about this already or someone can explain. I'll be out for a while.
Thank you very much for the info marcus.
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