TungstenTesla said:
Forgive me for being naive, but could someone explain how bounce models avoid the singularity? I thought the singularity was more or less assumed at this point.
The root meaning of "singularity" in mathematical science context is a failure of a man-made theory---a place where the model breaks down, blows up, fails to give meaningful numbers.
Popular literature, stimulating public imagination, has given a different meaning to the word just in unprofessional context.
But there have been singularities at various times in several different branches of physics. No one takes this as a sign that NATURE has a glitch

Historically, the singularity eventually is RESOLVED or cured by improving/replacing whatever theory had the trouble.
The cosmo singularity is specifically a trouble with the 1915 theory of General Rel. People are now in the process of fixing the trouble. This will make the singularity go away, since it is by definition a failure of the theory, not of nature.
However it is convenient to use the failurepoint of the classic GR theory as a time-marker to DATE stuff. Like "one second after the singularity" or "100,000 years after the singularity".
One doesn't assume that a singularity occurred in Nature, but it gives a good place to put the zero of the time-line. Everybody uses the classic model and knows where it fails.
It's like other conventional zeros. like 0 AD. A clear visible marker.
There's a German research institute that has a public outreach website called "Einstein-online" which does a good job giving realistic explanations, without the usual hype. I keep the link in my signature at the end of the post. They have an essay there called
A Tale of Two Big Bangs.
That essay explains the two senses----working cosmologists use it as a conventional zero, but do not expect that time actually stops there, as you go back. Read the essay for more clarification.
If you want to get caught up on early-universe research check out the proposals for the B-Pol and CMB-Pol missions. These may or may not get funding depending on economic conditions. They would be the next step after the Planck mission (currently in orbit, taking data.) Here for instance is the B-pol website. It has a menu with brief sections explaining the science and the instruments.
http://www.b-pol.org/index.php
These space observatories would be sensitive to
polarization in the ancient light of the CMB (cosmic microwave background). This is what the "Pol" in B-Pol means.
Probably the best introduction to leading edge observational cosmology of the early universe is to read the non-technical parts of a paper that just came out by
Julien Grain, Aurelien Barrau, Thomas Cailleteau, Jakub Mielczarek. Read the first few paragraphs at the beginning and the conclusion section at the end. Those parts are easy--no math. I'll get the link:
http://arxiv.org/abs/1011.1811
Observing the Big Bounce with Tensor Modes in the Cosmic Microwave Background: Phenomenology and Fundamental LQC Parameters
Julien Grain, A. Barrau, T. Cailleteau, J. Mielczarek
12 pages, 5 figures
(Submitted on 8 Nov 2010)
"Cosmological models where the standard Big Bang is replaced by a bounce have been studied for decades. The situation has however dramatically changed in the last years for two reasons. First, because new ways to probe the early Universe have emerged, in particular thanks to the Cosmic Microwave Background (CMB). Second, because some well grounded theories -- especially Loop Quantum Cosmology -- unambiguously predict a bounce, at least for homogeneous models. In this article, we investigate into the details the phenomenological parameters that could be constrained or measured by next-generation B-mode CMB experiments. We point out that an important observational window could be opened. We then show that those constraints can be converted into very meaningful limits on the fundamental Loop Quantum Cosmology (LQC) parameters. This establishes the early universe as an invaluable quantum gravity laboratory."
Chronos already gave some relevant links and is giving the correct information in this thread---I don't want to get further involved but just give some backup detail.
BTW I think this thread should better have been started in Cosmology forum. How the U got started is part of what cosmology studies. It really helps to keep the topics sorted more or less consistently. You'll find that out if you stick around long enough.