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El Naschie, M.S. (2015) Mathematical Models and Methods in Dark Energy Theory: Dvoretzky’s Theorem, Casimir Effect, Mobius Geometry. Problems of Nonlinear Analysis in Engineering Systems, 2, 1-16. (University of Kazan Press, Russia, Published in Russian and English language versions)

has been cited by the following article:

• TITLE: Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos

  AUTHORS: Mohamed S. El Naschie

  KEYWORDS: Dark Energy, Accelerated Cosmic Expansion, Hyperbolic Geometry, Fractal Geometry, Transfinite set Theory, ‘tHooft Dimensional Regularization, Hardy’s Quantum Entanglement, Davis Hyperbolic Manifold, Compactified Klein Modular Curve, Fractal Counting, Lie Symmetry Groups, Stein Spaces

  JOURNAL NAME: Natural Science, Vol.8 No.3, March 17, 2016

  ABSTRACT: The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.