Marcus, I agree the multiverse is a vague concept. In the LQC bounce the prior contracting phrase is considered pretty similar (even mirror image) to our universe. However our universe does not look like its going to recollapse so there has to be something significantly different about the contracting branch even if its just the distribution of matter/dark matter/dark energy. The only way to get the contracting universe to be the same as our universe is if we assume dark energy is not a constant but something dynamical, do you agree? I don’t think we can rule out dynamical dark energy, but right now it looks like a constant, probably the cosmological constant.
I also agree:
"All I’m saying is that the conclusion that inflation is eternal is a result of a calculation of how [SOME] inflationary theorists think the [SOME TYPE OF] inflaton field evolves..."
Even Guth says almost all inflationary models are eternal, rather than all.
I can’t match your understanding of the literature but I can give my journalistic instinct. Eternal inflation is one of many models of what happened in the very early universe. Most of the originators of inflationary cosmology Guth, Steinhardt, Linde etc think that if inflation happened its eternal. There is a huge pop science interest in the multiverse. I think string theory would have been killed when the landscape was discovered but managed to survive only because eternal inflation allowed them to populate their landscape. So whether inflation is eternal or not is a very big story.
The critics of inflation make at least two major points, inflation:
1 requires fine tuning to start so doesn’t solve the problems it’s advertised to
2 is eternal and hence loses predictivity
Along comes LQC and these guys are clearly saying problem 1 is solved. But yet I don't seem them saying problems 2 is solved.
I asked the researchers I spoke to about this, none of them have made that claim. The closest I’ve got is Abhay Ashtekar saying problem 2 might get solved in the future. But even if this is going to happen, he left open whether LQC would confirm or deny eternal inflation saying he had no intuition about it.
Also Aurélien Barrau has said the multiverse should be taken seriously:
http://cerncourier.com/cws/article/cern/31860
and he invoked ternal inflation.
So if his new results overturned this I’m sure it would be big news.
I can’t follow the maths in these papers as well as you and I really appreciate your input but reading the conclusions, but I just don’t see anything in LQC inflation papers that overturns eternal inflation. Of course that doesn’t mean eternal inflation is true but I’m not so sure that LQc has put the nail in its coffin.
Recently Abhay Ashtekar gave a talk to the joint Tufts/Mit seminar, Alan Guth and Alex Vilenkin. I wonder what the q&A was like? Have you spoken to Aurélien Barrau about it? I think he’s going to be at loops 2013 so if you are going to be there , it will very interesting to see what he has to say. If not maybe Ill email him, let me know.