S_McLachlan said:
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Marcus, if you have links to research i'd very much appreciate it.
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Stuart, my answer will be a bit roundabout. Looking over the field from various viewpoints before picking one particular research paper. Or perhaps you will pick one for yourself.
With research papers, as you may know, even a fairly technical one can have stuff in ordinary English in the introduction section and in the conclusions paragraph at the end. Also just scanning titles and abstracts can give some idea of what's going on in a field. So if you like technical reading, great, and if not you may still get some clues from this.
A research area where among other things they model the start of expansion with models that don't break down and develop a singularity is called Quantum Gravity. The subfield is Quantum Cosmology. (When you quantize you can avoid the breakdown of the classical model.) These days I'm especially interested in watching QC phenomenology.
So I constructed this Spires search:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29
It is not perfect. It gets some stuff that I'm not interested in. But it's still pretty good. I'm only interested in recent QC pheno so I set "DATE>2008" which means all the papers are 2009 or later.
Phenomenologists look for ways to TEST and study the effectiveness of various observational tests. Early universe pheno people have gotten interested in Loop QC, which predicts a bounce, with certain characteristics. And they are asking what can we look for now in the CMB ancient light that would allow us to constrain or rule out or somehow test for the Loop QC bounce?
If you click on that Spires search you see a bunch of that kind of paper. Barrau, Grain, Wen Zhao, Mielczarek, Tsujikawa, Cailleteau are phenomenologists. They don't have a professional stake in Loop, their business is testing. Some of the papers are by pheno people, and some are by Loop people (like Ashtekar, Sloan, Corichi, Wilson-Ewing.)
Loop QC has a clear enough explanation for the start of expansion because the Loop people found a way to quantize the basic equation of cosmology where quantum effects cause gravity to be repellent at high density. So they put their model in the computer and run time backwards and find a prior collapsing phase and a bounce. The expansion gets kicked off in a very clear way. Then as soon as density goes back down the model converges to classical behavior and continues on the familiar track. The regime where quantum effects dominate is where the density is around 1 percent of Planck density or greater. The bounce happens at around 40% of Planck density.
The key thing now is to test. It may require putting some new intruments in orbit, to map the polarization of the CMB in finer detail than is currently possible. It may be possible to constrain LQC or even rule it out. Or it may pass the first observational tests.
So that's one thing.
Another thing is to look at the whole field of Quantum Cosmology. Here is a Spires search with the same date restriction of DATE>2008. This is a very broad search and does not pick out papers with a Phenomenology focus. It gets 245 papers of all QC kinds (not just bounce-type and not only Loop).
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=dk+quantum+cosmology+and+date+%3E+2008&FORMAT=WWW&SEQUENCE=citecount%28d%29
You might look down the first 20 or 30 (or 50 why not?) on the list of titles to get an impression of what the main topics are and who the main authors are of the more highly cited papers. The more highly cited ones are listed first.
I'd rather not point to one specific paper until you have had a chance to get a general impression of what research is going on. Also do you have any questions about what ypu see in these Spires searches?