Hello,

What do you mean exactly by collapse ? If you take a chunk of matter and apply enough compression, you get different states of matter. If your compression is extreme, you might overcome natural barriers (coulomb barrier, etc) so that quark bonds become more and more loose (imagine a rubber band for the strong force bond). Eventually, your chunk of matter won't look too good since it will become some sort of quark-gluon plasma. There are numerous experiments and papers on the subject. Just check out www.bnl.gov/rhic and you'll understand what's at stake. They collide heavy ions (like gold) inside a big ring shaped collider to create this particular state of matter and prove experimentally that matter can undergo a phase transition from hadronic to partonic. Also check out the LHC (large ion collider) project at CERN.

Now, if you mean a collapse due to gravity overcoming the nuclear push inside a star, we now have good evidence of the existence of black holes and neutron stars. In the latter case, the term 'neutron' is a bit misleading. It is true that the star is composed of highly compressed matter in which neutrons are a big part of, but don't get fooled by this. In fact, this state of matter is better described as : highly compressed hadronic matter. Hydrogen would not survive at all in this environment. In fact, there was recently a claim that certain neutron stars could even have in their core some quark-gluon plasma, namely the state of matter of the very early universe. But it turns out that the claim was a bit too enthusiastic ... too bad ...

Finally, if you now mean the collapse of all matter in the universe, as opposed to stationary state theories, that remains to be proved. Don't forget that the big bang theory is experimentally evidenced by mainly two observations :
1- red-shift
2- cosmic background radiation

But even these two observations are now under scrutiny and many physicists claim or even made observations that contradict the common interpretation of these two key proofs. I don't have any link to provide right now but if anyone is interested I can look it up at home (I am still at work now).