Author(s)

Mohamed S. El Naschie

Department of Physics, University of Alexandria, Alexandria, Egypt.

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.

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

El Naschie, M. (2016) Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos. Natural Science, 8, 152-159. doi: 10.4236/ns.2016.83018.