 Quote by marcus
Or you could jump in and have a look at the listing that you get with a "quantum cosmology" keyword search at a professional research library. Here are 379 papers in QC that appeared in 2009 or later, ordered by number of times the paper has been cited in other research. (citecount is a rough indicator of importance, so you tend to get the most significant papers listed first).
http://www-library.desy.de/cgi-bin/s...tecount%28d%29
This search simply uses the keyword "quantum cosmology" so you get all kinds of quantum cosmology. However the first 30 or 40 papers are mostly all "loop" qc (LQC). That's a particular type of model that a lot of people are currently working on. LQC goes back before the big bang in a fairly straightforward way---quantize the normal cosmology equation to include quantum effects working at extremely high density, so then the model does not fail mathematically and you can crank on back in time thru a kind of "bounce" and get to a familiar type of universe like what we see except contracting.
If you look further on the list, past the first 30 or so you will find OTHER kinds of quantum cosmology models, not only LQC...
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 Quote by jackmell
So basically just a bounce? Is that all? And how would a Universe like ours but contracting behave?...
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That's right, the simplicity of the model is one of the most appealing things about it. The contracting phase behaves as an ordinary classical universe (same physical laws) until quantum corrections to GR take over very close to bounce.
The key person in this context is Abhay Ashtekar, who discovered an equivalent formulation of General Relativity (around 1980) which has become the basis for the canonical quantization of GR that was adapted for Quantum Cosmology.
Here's a New York Times piece on Ashtekar.
http://www.nytimes.com/1999/04/20/sc...d=print&src=pm
An essential point is that when GR is formulated using "Ashtekar variables" and quantized, there are quantum corrections to gravity. In the quantum cosmology developed by Ashtekar and others (see the literature list in post #15) at extreme density quantum effects dominate and gravity becomes repellent. There is a non-equilibrium regime where the universe continues to contract (as if by a kind of momentum) even though gravity is repelling and trying to force everything apart---black holes are coming unbound and smoothing out, the geometry is trying to be as uniform and even as possible.
This repellent effect of quantum gravity at extremely high density eventually stops the collapse and causes a rebound. By that time the metric and matter are smooth, evened out, by the non-equilibrium process I described.
Since 2006 there has been a lot of numerical simulations of the bounce by Ashtekar's group. You may be able to find more if you google Ashtekar or search for his papers in the preprint archive:
http://arxiv.org
Here is my post #15 which has QC papers from 2009 to present.