skydivephil said:
... But in those loop scenarios that do have cycles, what is that makes the acceleration of the universe we currently observe slow down and turn around?
Just simple gravity. You only get the model to behave that way when you set the mass density unrealistically high.
You may remember before 1998 when people assumed Lambda=0 the cosmology textbooks always talked about 3 distinct scenarios closed/flat/open. The "closed" scenario had the mass density above some critical value making the U both spatially closed AND destined to eventually crunch.
Now, with Lambda>0 we can have a model that is spatially closed BUT expands indefinitely.
In 2006 when the Penn State people started doing computer simulations to try out their new dynamics they kept it simple. So in effect they were back in pre-1998 cosmology. And one of the behaviors they wanted to reproduce was the "closed" case where you naturally get recollapse.
That's fine, it was a conscious choice to keep it simple and not try to do everything at once. It was also a chance to test the code and learn about behavior right around the bounce. So they ran these periodically bouncing cyclic cases. And they also ran a socalled "flat" or k=0 case where you just get one bounce and expansion if forever but just barely.
I forget when they started to put in inflation, probably around 2009 or 2010.
And Lambda only has a late time effect, in the early universe its effect is vanishingly small because radiation and matter dominated. So you include it in the theory but can neglect it if you are doing numerical simulation of behavior right around the bounce.
Also Planck's cosmological results are due in about 6 months, do we have any clean set of predictions from LQC that don't rely on discovering the B mode and are different to the 7 year WMAP results? I have to say my main fear for Planck is that it will just be WMAP to more decimal places. Perhpas we need a dedicated B mode mission?
A number of people have said we need a dedicated B mode mission. I think NASA had a request for proposals out sometime before 2008. there was talk of a "CMB-pol" mission focusing on polarization of the CMB map. You may know more about this. There was a paper by Wen Zhao and two people at Cambridge that made the argument "look we can already constrain the models with the data we have, but we could constrain them so much b better if we had an detailed map of the polarization!" But then there were budget problems and a lot of cuts.
I think what you are talking about is still on the agenda, just put on the back burner because of funding limitations. But I'm out of touch, and just infer stuff from what I read, you may know better. "CMB-pol" or sometimes referred to as "B-pol" seems like an obvious mission as soon as the funding situation improves. So I don't worry about it.
(I might worry about superrich moneypower ending democracy in America, rather than the delay of sensible science missions.

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What you say about Planck mission is interesting. I simply do not know what and how much new science to expect from Planck. I am personally very optimistic. When you say "more decimal places" that is after all what it is about. WMAP already constrains Loop cosmology.
I feel sure Planck will further narrow down the acceptable range of parameters.
You've probably seen this list of some 60 papers mostly of a Loop phenomenology character but I'll get the link in case others who haven't seen it might be reading. All these papers are recent---appeared 2009 or later. Many of these people are saying what to look for in Planck mission data. It's not, as you say, CLEAN. But that's life. A lot of people are busy on it and we'll just have to see when the dust settles. Sometimes this link is slow and I just wait. Sometimes it doesn't work but does when I come back to it later. I just tried it and it worked:
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
(desy spires is better in some respects than the new system inspire)