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

摘要

The following document is to answer if higher dimensions add value to answeringfundamental cosmology questions. The results are mixed, 1st with higher dimensions apparentlyhelping in reconstructing and preserving the value of Planck’s constant, and the fine structureconstant from a prior to a present universe, while 2nd failing to add anything different fromfour dimensional cosmological models to the question of what would cause an increase inthe expansion rate of the universe, as of a billion years ago. Finally 3rd, higher dimensionsmay allow creation of a joint DM and DE model. A choice between LQG and brane worldgeometry is introduced by Snyder geometry, where Snyder geometry’s minimum uncertaintylength calculations Δx may help determine to what extent gravity is an emergent field thatis classical. Independent of the choice of LQG and branes (four dimensions versus higherdimensional cosmology models) is the following question: If gravity is largely classical, howmuch nonlinearity is involved? Gravitons and their structure as information carriers may helpanswer these questions. The main point of this document: DM and DE may be unified in termsof cosmological dynamics if the higher dimensional models of DM, as seen by KK towers ofgravitons are seen to be pertinent to increasing acceleration of the universe a billion years agovia a 4th dimensional small graviton mass term added to the KK tower DM representation ofgravitons (a model of DM).