Snyder Geometry, Loop Quantum Gravity and Brane Worlds

Andrew W Beckwith
(American Institute of Beam Energy Propulsion, USA)


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In Loop Quantum Gravity (LQG) the entropy of Standard Model black holes is of order 10^{89}, with pronounced implications for the classical singularities of general relativity. Recent papers in LQG, which the author was exposed to at the 12th Marcel Grossman conference, assumed that big bounce replaced the singularity conditions of Hawking, Ellis, and others. In particular, Marco Valerio Battisti [ Phys. Rev. D 79 (2009) 083506] uses Snyder geometry to find a common basis in which to make a limiting approximation to derive either braneworld or LQG conditions for cosmological evolution. The heart of what Battisti works with is a deformed Euclidean Snyder space.

We will use this result explicitly to establish criteria for information transfer from a prior to a present universe. In this way one may, on falsifiable experimental grounds, determine whether minimal spatial uncertainty requirements for space time can distinguish between LQG and brane world scenarios. The tie in with entropy and information processing comes in via order of magnitude estimates of the minimum informational content needed to preserve continuity of basic physical laws between our present and a past cosmos. Continuity would be preserved in physical laws if the fundamental physical constants of nature remain invariant.