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General Relativity And Quantum Cosmology

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Posted by Richard Ruquist on October 14, 2004 13:41:01 UTC

General Relativity and Quantum Cosmology(GR_QC)

Any student concerned with the theoretical understanding of both the Big Bang and Black Holes should at least on a weekly basis read the publications in this field that appear on the Cornell Archives. Almost every publication in this field first appears here. A internet address of the GR_QC archive is:

This past week several really interesting papers appeared there. Foremost in my mind, as a student in this field, is the review paper for non-experts of Abhay Ashtekar on loop quantum gravity located at:

The term loop quantum gravity now seems to be changing to Quantum Einstein Gravity(QEG). Seems that this field gets more status if it's name follows the QED, QCD format. QEG derives spacetime rather than postulating it, as I previously thought string theory did, which I now suppose should be called Quantum String Dynamics(QSD).

However, I recommend reading how spacetime can be derived from String Theory in a paper by Gary Horowitz at: So spacetime is not necessarily a postulate of string theory.

Then in something I find amusing, Woodside has demonstrated how to derive spacetime from electromagnetic theory at: This paper is not so readable and I cannot ascertain its validity. Anyway the Ashetaker paper is a great intro to the fundamentals of spacetime and may help you to understand both Horowitz’s and Woodsides’s paper. Woodsides paper does away with Dark Matter, by the way.

For any of you familiar with my posts on the G&S subforum, you know that Dark Matter(DM) is close to my heart. Yet first Moffatt, then Cahill and now Woodside have derived modified GR theories where Dark Matter is a figment of incomplete GR theory. Well, in this same last week, there appeared in the archives a paper from China suggesting that Dark Energy(DE) can sustain density variations: Maybe it's all DE.

For your convenience the Abstracts of these papers are copied below.
Gravity and the Quantum
Authors: Abhay Ashtekar
Comments: A general review of quantum gravity addresed non-experts; for a special 2005 collection
The goal of this article is to present a broad perspective on quantum gravity for \emph{non-experts}. After a historical introduction, key physical problems of quantum gravity are illustrated. While there are a number of interesting and insightful approaches to address these issues, over the past two decades sustained progress has primarily occurred in two programs: string theory and loop quantum gravity. The first program is described in Horowitz's contribution while my article will focus on the second. The emphasis is on underlying ideas, conceptual issues and overall status of the program rather than mathematical details and associated technical subtleties.
Spacetime in String Theory
Authors: Gary T. Horowitz
Comments: 20 pages
We give a brief overview of the nature of spacetime emerging from string theory. This is radically different from the familiar spacetime of Einstein's relativity. At a perturbative level, the spacetime metric appears as ``coupling constants" in a two dimensional quantum field theory. Nonperturbatively (with certain boundary conditions), spacetime is not fundamental but must be reconstructed from a holographic, dual theory.
Quantum Gravity at Astrophysical Distances?
Authors: M. Reuter, H. Weyer
Comments: 43pp, 4 figures
Report-no: MZ-TH/04-15
Assuming that Quantum Einstein Gravity (QEG) is the correct theory of gravity on all length scales we use analytical results from nonperturbative renormalization group (RG) equations as well as experimental input in order to characterize the special RG trajectory of QEG which is realized in Nature and to determine its parameters. On this trajectory, we identify a regime of scales where gravitational physics is well described by classical General Relativity. Strong renormalization effects occur at both larger and smaller momentum scales. The latter lead to a growth of Newton's constant at large distances. We argue that this effect becomes visible at the scale of galaxies and could provide a solution to the astrophysical missing mass problem which does not require any dark matter. We show that an extremely weak power law running of Newton's constant leads to flat galaxy rotation curves similar to those observed in Nature. Furthermore, a possible resolution of the cosmological constant problem is proposed by noting that all RG trajectories admitting a long classical regime automatically give rise to a small cosmological constant.
Space-time Curvature of Classical Electromagnetism
Authors: R. W. M. Woodside
Comments: 26 pages, 18 references, submitted to GRG
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined with De Rham co homology theory. Radiative electromagnetic fields must be exact and co exact to preclude unobserved massless topological charges. Weyl's conformal tensor, here called ``the gravitational field'', is decomposed into a divergence-free non-local piece with support everywhere and a local piece with the same support as the matter. By tuning a local gravitational field to a Maxwell field the electromagnetic field's local gravitational field is discovered. This gravitational field carries the electromagnetic field's polarization or phase information, unlike Maxwell's stress-energy tensor. The unification assumes Einstein's equations and derives Maxwell's equations from curvature assumptions. Gravity forbids magnetic monopoles! This unification is stronger than the Einstein-Maxwell equations alone, as those equations must produce the electromagnetic field's local gravitational field and not just any conformal tensor. Charged black holes are examples. Curvature of radiative null electromagnetic fields is characterized.
Anthropic Principle Favors the Holographic Dark Energy
Authors: Qing-Guo Huang, Miao Li
Comments: 10 Pages
We discuss the anthropic principle when applied to the holographic dark energy. We find that if the amplitude of the density fluctution is variable, the holographic dark energy fares better than the cosmological constant.

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