http://arxiv.org/abs/gr-qc/0601085
Loop Quantum Cosmology
Martin Bojowald
104 pages, 10 figures; online version, containing 6 movies, available at "Living Reviews":
http://relativity.livingreviews.org/Articles/lrr-2005-11/
AEI-2005-185, IGPG-06/1-6
Journal-ref: Living Rev. Relativity 8 (2005) 11
"Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time."
To get the movies, go to the Living Reviews version
http://relativity.livingreviews.org/Articles/lrr-2005-11/
and scroll down the sidebar menu all the way to the bottom where it says "figures"
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Also in today's arxiv postings:
http://arxiv.org/abs/gr-qc/0601082
Quantum Hamiltonian for gravitational collapse
Viqar Husain, Oliver Winkler
17 pages
"Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion operators presented in an earlier work, form a framework for studying gravitational collapse in quantum gravity. We describe a setting for its numerical implementation, and discuss some conceptual issues associated with quantum dynamics in a partial gauge fixing."
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Lee Smolin thinks that if MOND is real then it may have an explanation in quantum gravity. We should keep an eye on MOND research, just in case.
Here is an overview for beginners. Good place to start if you want to learn something about MOND.
http://arxiv.org/abs/astro-ph/0601478
Modified Newtonian Dynamics, an Introductory Review
Riccardo Scarpa
"By the time, in 1937, the Swiss astronomer Zwicky measured the velocity dispersion of the Coma cluster of galaxies, astronomers somehow got acquainted with the idea that the universe is filled by some kind of dark matter. After almost a century of investigations, we have learned two things about dark matter, (i) it has to be non-baryonic -- that is, made of something new that interact with normal matter only by gravitation-- and, (ii) that its effects are observed in stellar systems when and only when their internal acceleration of gravity falls below a fix value a0=1.2x10-8 cm s-2. This systematic, more than anything else, tells us we might be facing a failure of the law of gravity in the weak field limit rather then the effects of dark matter. Thus, in an attempt to avoid the need for dark matter, the Modified Newtonian Dynamics. MOND posits a breakdown of Newton's law of gravity (or inertia) below a0, after which the dependence with distance became linear. Despite many attempts,
MOND resisted stubbornly to be falsified as an alternative to dark matter and succeeds in explaining the properties of an impressively large number of objects without invoking the presence of non-baryonic dark matter. In this paper, I will review the basics of MOND and its ability to explain observations without the need of dark matter."
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Of possible interest to the category-minded:
http://arxiv.org/abs/math.QA/0601458
Categorified Algebra and Quantum Mechanics
Jeffrey Morton (University of California, Riverside)
67 pages, 25 figures
Jeffrey Morton has studied Quantum Gravity with
John Baez. Here is what he says in the acknowledgments section
"This work grew out of the regular Quantum Gravity seminar taught by
John Baez at UCR, notes for which are available online as [2]. I would like to acknowledge his work on this subject (some published as [1]), excellent teaching, and helpful advice and discussions in preparing this paper. Other students in the seminar, especially Toby Bartels, Miguel Carrion-Alvarez, Alissa Crans, and Derek Wise also provided many useful discussions."
We know Miguel and Derek as Baez QG students. Miguel recently finished his thesis and Derek gave a paper at Loops '05. So this comes out of that group, although it is not specifically about gravity.