Several postings about solvable LQC-and other news

[marcus]

Several postings about solvable LQC--and other news

AFAICS cosmology is the main prospective proving ground for quantum gravity---cosmology and astrophysical observation generally.

A LQG explanation for the dark energy effect (accelerating expansion as the cumulative result of quantum corrections) has been proposed. Likewise a various mechanisms to account for inflation have come up in Loop and other QG. There has been a lot of discussion of gammaray observations (MAGIC, GLAST...) probing QG and testing various models.

Various LQG ways of resolving BB and BH singularities are being explored and have sparked debate. Observable effects (on GRBs, on the universe's largescale structure) have been suggested, to look for as ways of testing the various models that replace classical singularities.

The upshot is that you can't really separate LQG from either its phenomenology (which so far is mostly in astronomy though some might come up in LHC) or its application to cosmology and the resolution of classical singularties.

It's all one package.

When we look at the whole cluster of research activity certain salient things stand out
and help define what is going on at present

1. Smolin et al's ball and tube method for defining a quantum state of geometry and matter (Yidun W., Louis K, Sundance BT, Jonathan H are among those currently working on this). More info: https://www.physicsforums.com/showthread.php?t=190053

2. Rovelli et al's Marseille new vertex. Defines a new LQG spinfoam model. Surprising agreement with LQG area spectrum, and earlier LQG in general, signs of correct semiclassical limit. Most people involved with this are in Rovelli's group at Marseille, but closely related variants are being worked on at several other places. More info: https://www.physicsforums.com/showthread.php?t=194651

3. Ashtekar et al's solvable LQC model (Corichi, Pawlowski, Singh are among those working on this.)

I guess you could say that the big LQG tent contains a three-ring circus (Perimeter ball-and-tube, Marseille new vertex, Penn State solvable LQC.
That would make Martin Reuter's asymptotic safety a sideshow outside the main tent.
It gets a bit tricky at times trying to watch all the action.

==============
Anyway here's an update on #3 in the above list.

There's a series of papers coming out. Two have already posted on arxiv, two are in preparation but I can say a bit about them, and there may be others.
Corichi uses the acronym sLQC for solvable LQC model---which might catch on. It sounds like "slick", in case that helps you remember it.

The point about sLQC is that it is simplified, so it leaves open the question of whether the results would be generic for the full theory----and robustly carry over to messier, more realistic cosmology. However with that reservation, sLQC does seem to allow inference of conditions before the big bang.

 

[marcus]

http://arxiv.org/abs/0710.3565
On the robustness of key features of loop quantum cosmology
Abhay Ashtekar, Alejandro Corichi, Parampreet Singh
28 pages, 1 figure
(Submitted on 18 Oct 2007)

"A small simplification based on well motivated approximations is shown to make loop quantum cosmology of the k=0 FRW model (with a massless scalar field) exactly soluble. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying LQC is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity."


http://arxiv.org/abs/0710.4543
Quantum bounce and cosmic recall
Alejandro Corichi, Parampreet Singh
4 pages
(Submitted on 24 Oct 2007)

"Loop quantum cosmology predicts that, in simple models, the big bang singularity of classical general relativity is replaced by a quantum bounce. Because of the extreme physical conditions near the bounce, a natural question is whether the universe can retain, after the bounce, its memory about the previous epoch. More precisely, does the universe recall various properties of the state after evolving unitarily through the bounce or does it suffer from cosmic amnesia as has been recently suggested? Here we show that this issue can be answered unambiguously by means of an exactly solvable model, derived from a small simplification of loop quantum cosmology, for which there is full analytical control on the quantum theory. We show that if there exists a semi-classical state at late times on one side, peaked around a pair of canonically conjugate variables, then there are very strong bounds on the fluctuations on the other side of the bounce, implying semi-classicality. For a model universe which grows to a size of 1 megaparsec at late times, the change in relative fluctuations of the only non-trivial observable of the model across the bounce is less than 10^-57 (becoming smaller for universes which grow larger). The universe maintains (an almost) total recall."

About the possible two other papers still in preparation, one of them addresses the issue of INFLATION. This paper, by Ashtekar, Pawlowski and Singh, is expected to show that their way of resolving the BB singularity allows for adequate inflation. For some decades there has been a widely accepted estimate of exp(60) as the necessary inflation factor---adequate to take care of the various jobs that inflation scenarios were invented to take care of. Apparently there was some question as to whether their model could accommodate an "inflaton" potential and still behave right---and this has now been resolved.

I believe there is yet another paper by Corichi and Singh in the works which is part of the sLQC "recall versus amnesia" debate with Martin Bojowald. This kind of rapid-fire exchange of papers seems to be good for research and for the level of interest in the field.

 

[Entropia]

This is something that quantum cosmology has long promised but never delivered on. In the sLQC model, the big bang is resolved and the big bang state is not a singularity but a state with well-defined quantum geometric properties. This is a big step forward for quantum cosmology.
Thank you for sharing this information about the current state of research in Loop Quantum Gravity (LQG). It is fascinating to see the progress being made in this field and the potential applications in cosmology and astrophysics.

I find it particularly interesting that LQG is being explored as a potential explanation for dark energy and inflation, and that there are ongoing efforts to test these theories through observations. It is also exciting to see that LQG is providing potential solutions to long-standing problems in cosmology, such as the singularity at the beginning of the universe.

I agree that it is important to consider the limitations of simplified models like sLQC, but it is still a significant step forward in understanding the quantum nature of the universe. It will be interesting to see how these results hold up in more complex and realistic scenarios.

Overall, it seems that LQG is a rapidly developing and dynamic field of study, with multiple research groups and approaches working towards a better understanding of quantum gravity. I look forward to following the progress and potential implications of these advancements.