marcus
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tom.stoer said:...
- LQG footprint in CMB due to primordial gravitational waves is only be derived within LQC (**)
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(** this sems to be the most promising research area, but afaik it is unclear if full LQG will reproduce the LQC predictions)
I agree that it is the most promising. It sounds to me like the big issue for you is whether full LQG will reproduce the LQC predictions.
I keep seeing research in that direction which seems to be making progress. So to satisfy you that LQG is as testable as LQC I need to start keeping better track of those particular papers.
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BTW I should report that, contrary to my expectations and perhaps prejudices, when I had a look in the literature just now the FIRST author I found working on Lqg --> Lqc
was a guy working for Steve Carlip at UC Davis. Carlip is an excellent quantum relativist who has PhD students working in several QG including LQG, "shape dynamics", and CDT.
I heard Carlip talk on QG spontaneous dimensional reduction here at Berkeley and hold him in high regard. He has this student Chun-yen Lin.
PhD thesis --- http://arxiv.org/abs/0912.0554 (revised March 2011)
November 2011 followup --- http://arxiv.org/abs/1111.1766
Emergence of Loop Quantum Cosmology from Loop Quantum Gravity: Lowest Order in h
I don't know if the work is good, but I was surprised to see it uses the
canonical Lqg approach. You have to figure that Carlip (who is world class) is guiding this guy. He seems to be still at UC Davis even though probably now post-doc. Here is Chun-yen Lin's conclusion paragraph:
==quote 1111.1766==
This paper starts from the kinematical Hilbert space of loop quantum gravity, which describes the matter fields living in the dynamical quantum geometry of space. Using the model with a modified Hamiltonian constraint operator, we see that the dynamics of such a system reproduces FRW cosmology in the large scale limit. Further, the O(h0) corrections of the model for FRW cosmology conform with loop quantum cosmology in a specific scheme. Such a result is valuable, since it attributes the predictions of loop quantum cosmology to the fundamental principles in loop quantum gravity.
The result serves as a starting point to many possible future projects. First, one may explicitly construct the coherent states in the model to evaluate the emergent cosmology beyond O(h0), to get the quantum fluctuation corrections in the emergent cosmology. Second, one may try to derive more of the implications of loop quantum cosmology by applying the model to more realistic cosmological settings. Third, one may try to improve the model by incorporating the graph-topology changing feature in the Hamiltonian constraint operator, in the hope of deriving loop quantum cosmological models with μ = μ ̄.
==endquote==
Well nobody is saying that the job is finished! But I see he has made a little progress. He gets a bounce with his Lqg model and estimates the matter density and it higher than the density at bounce that Ashtekar gets in regular Lqc, but at least not grossly lower as one might have feared. Plenty of work left to do here.
And there are also other Lqg --> Lqc papers which I should gather to get an idea of how the research is going on this front.
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