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Comments on this thread remind me that LQC has progressed quite a bit in the past 2 or 3 years and it is not so easy to keep abreast. So I want to call attention to a Abhay Ashtekar's recent review paper---a kind of status report---and quote some interesting passages just to get the latest stuff out on the table.
http://arxiv.org/abs/1108.0893
Loop Quantum Cosmology: A Status Report
Abhay Ashtekar, Parampreet Singh
(Submitted on 3 Aug 2011)
The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that, as described at the end of section I, each of these communities can read only the sections they are most interested in, without a loss of continuity.
138 pages, 15 figures. Invited Topical Review, To appear in Classical and Quantum Gravity.
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The paper is long and covers many topics. We already had a discussion here at PF forum of one of the key equations. Equation (5.7) as I recall. I forget who was asking about it.
Yes! It was (5.7) on page 73. This is the modified form of the Friedman equation which comes out of quantizing it and it shows clearly why you get gravity repelling at high density and causing a rebound (with an interval of super-exponential expansion called super-inflation).
That however is not new, one sees that modified Friedman derived already in 2007 basic LQC papers. (Together with a figure for the critical density at which the quantum corrections dominate.) So I won't copy that here.
What I want to take note of is some more recent stuff about generalizing and extending the model that they go into around page 67. Don't have time right now but hope to get back to this later today.
http://arxiv.org/abs/1108.0893
Loop Quantum Cosmology: A Status Report
Abhay Ashtekar, Parampreet Singh
(Submitted on 3 Aug 2011)
The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that, as described at the end of section I, each of these communities can read only the sections they are most interested in, without a loss of continuity.
138 pages, 15 figures. Invited Topical Review, To appear in Classical and Quantum Gravity.
=======================
The paper is long and covers many topics. We already had a discussion here at PF forum of one of the key equations. Equation (5.7) as I recall. I forget who was asking about it.
Yes! It was (5.7) on page 73. This is the modified form of the Friedman equation which comes out of quantizing it and it shows clearly why you get gravity repelling at high density and causing a rebound (with an interval of super-exponential expansion called super-inflation).
That however is not new, one sees that modified Friedman derived already in 2007 basic LQC papers. (Together with a figure for the critical density at which the quantum corrections dominate.) So I won't copy that here.
What I want to take note of is some more recent stuff about generalizing and extending the model that they go into around page 67. Don't have time right now but hope to get back to this later today.