Relativity and Cosmology


Applications of Euclidian Snyder Geometry to the Foundations of Space Time Physics

Authors: Andrew Beckwith

The following document is to answer if higher dimensions add value to answering fundamental cosmology questions. The results are mixed, 1st with higher dimensions apparently helping in reconstructing and preserving the value of Planck's constant, and the fine structure constant from a prior to a present universe, while 2nd failing to add anything different from four dimensional cosmological models to the question of what would cause an increase in the expansion rate of the universe, as of a billion years ago. Finally 3rd, higher dimensions may allow creation of a joint DM and DE model. A choice between LQG and brane world geometry is introduced by Snyder geometry, where Snyder geometry's minimum uncertainty length calculations δx may help determine to what extent gravity is an emergent field that is classical. Independent of the choice of LQG and branes (four dimensions versus higher dimensional cosmology models) is the following question: If gravity is largely classical, how much nonlinearity is involved? Gravitons and their structure as information carriers may help answer these questions. The main point of this document: DM and DE may be unified in terms of cosmological dynamics if the higher dimensional models of DM, as seen by KK towers of gravitons are seen to be pertinent to increasing acceleration of the universe a billion years ago via a 4th dimensional small graviton mass term added to the KK tower DM representation of gravitons (a model of DM).

Comments: 20 pages. Significant re dos of material on deceleration parameter q(z) on pages 3, 4, and also Appendix A ( just added ). Figure 1 re sized and re parameterized. Additional work done on rest of document to answer questions raised by participants in Beyond the Standard Model, 2010, and also major re dos of what is now Appendix D. Emphasis as as source document of information for some of the presentations for several conference presentations, including Beyond the Standard Model 2010, and SPESIF 2010, and Piers XIAN, 2010, as well as possibly either IDM 2010 in July, or DICE 2010 in September 2010.

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Submission history

[v1] 6 Dec 2009
[v2] 10 Dec 2009
[v3] 27 Dec 2009
[v4] 22 Jan 2010
[v5] 19 Feb 2010

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