APM  Vol.4 No.12 , December 2014
From Highly Structured E-Infinity Rings and Transfinite Maximally Symmetric Manifolds to the Dark Energy Density of the Cosmos
ABSTRACT
Starting from well established results in pure mathematics, mainly transfinite set theory, E-infinity algebra over operads, fuzzy manifolds and fuzzy Lie symmetry groups, we construct an exact Weyl scaling for the highly structured E-infinity rings corresponding to E-infinity theory of high energy physics. The final result is an exact expression for the energy density of the cosmos which agrees with previous analysis as well as accurate cosmological measurements and observations, such as COBE, WMAP and Planck. The paper is partially intended as a vivid demonstration of the power of pure mathematics in physics and cosmology.

Cite this paper
Naschie, M. (2014) From Highly Structured E-Infinity Rings and Transfinite Maximally Symmetric Manifolds to the Dark Energy Density of the Cosmos. Advances in Pure Mathematics, 4, 641-648. doi: 10.4236/apm.2014.412073.
References
[1]   Weibel, P., Ord, G. and Rossler, O., Eds. (2005) Spacetime Physics and Fractality. Festschrift in Honour of Mohamed El Naschie on the Occasion of His 60th Birthday. Springer, Vienna-New York.

[2]   Yang, C.N. (1987) Square Root of Minus One, Complex Phases and Erwin Schrodinger. In: Kilmister, C.W., Ed., Schrodinger—Centenary Celebration of a Polymath, Cambridge University Press, Cambridge, UK, 53-64.

[3]   Donaldson, S.K. and Kronheimer, P.B. (1990) The Geometry of Four Manifolds. Oxford University Press, Oxford.

[4]   Kodiyalam, V. and Sunder, V.S. (2001) Topological Quantum Field Theories from Subfactors. Chapma & Hall/Crc, London, UK.

[5]   'tHooft, G. (2005) 50 Years of Yang-Mills Theory. World Scientific, Singapore. http://dx.doi.org/10.1142/5601

[6]   El Naschie, M.S., Rossler, O.E. and Prigogine, I. (1995) Quantum Mechanics, Diffusion and Chaotic Fractals. Pergamon Press/Elsevier, Oxford.

[7]   He, J.-H. (2005) Transfinite Physics. China Scientific and Culture Publishing, Shanghai.

[8]   Sidharth, B.G. and Altaisky, M.V. (2001) Frontiers of Fundamental Physics. Kluwer Academic/Plenum Publishers, New York (see in particular 81-95).

[9]   Friedlander, E. and Grayson, D. (2005) Handbook of K-Theory. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-540-27855-9

[10]   Cartier, P., Julia, B., Moussa, P. and Vanhove, P. (2006) Frontiers in Number Theory, Physics and Geometry I. Springer, Berlin.

[11]   El Naschie, M.S. (2004) A Review of E-Infinity and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19, 209-236. http://dx.doi.org/10.1016/S0960-0779(03)00278-9

[12]   E-Infinity Group: E-Infinity High Energy Communication Nos. 1 to 90. E-Infinity Energyblogspot.com.

[13]   Baker, A. (2013) Close Encounters of the E-Infinity Kind. Journal of Homotopy and Related Structures, 9, 257-282.

[14]   El Naschie, M.S. (1995) Banach-Tarski Theorem and Cantorian Spacetime. Chaos, Solitons & Fractals, 5, 1503-1508.
http://dx.doi.org/10.1016/0960-0779(95)00052-6

[15]   El Naschie, M.S. (2011) Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry. Journal of Quantum Information Science, 1, 50-53.
http://dx.doi.org/10.4236/jqis.2011.12007

[16]   Yau, S.-T. (2010) The Shape of Inner Space. Basic Book—Perseus Book Group, New York.

[17]   El Naschie, M.S. (1997) Advanced Prerequisites for E-Infinity Theory. Chaos, Solitons & Fractals, 30, 636-641.

[18]   Argyris, J. and Ciubotariu, C. (1997) On El Naschie’s Complex Time and Gravitation. Chaos, Solitons & Fractals, 8, 743-751. http://dx.doi.org/10.1016/S0960-0779(97)00072-6

[19]   Sigalotti, L. and Mejias, A. (2006) The Golden Ratio in Special Relativity. Chaos, Solitons & Fractals, 30, 521-524.
http://dx.doi.org/10.1016/j.chaos.2006.03.005

[20]   El Naschie, M.S. (1994) On Certain “Empty” Cantor Sets and Their Dimensions. Chaos, Solitons & Fractals, 4, 293-296. http://dx.doi.org/10.1016/0960-0779(94)90152-X

[21]   Crasmareanu, M. and Hretcanu, C. (2008) Golden Differential Geometry. Chaos, Solitons & Fractals, 38, 1229-1238.
http://dx.doi.org/10.1016/j.chaos.2008.04.007

[22]   El Naschie, M.S. (1998) Von Neumann Geometry and E-Infinity Quantum Spacetime. Chaos, Solitons & Fractals, 9, 2023-2030.

[23]   El Naschie, M.S. (2007) On the Universality Class of All Universality Classes and E-Infinity Spacetime Physics. Chaos, Solitons & Fractals, 32, 927-936. http://dx.doi.org/10.1016/j.chaos.2006.08.017

[24]   El Naschie, M.S. (2014) Why E Is Not Equal to mc2. Journal of Modern Physics, 5, 743-750.
http://dx.doi.org/10.4236/jmp.2014.59084

[25]   El Naschie, M.S. (2008) Average Exceptional Lie Group Hierarchy and High Energy Physics. American Institute of Physics Conference Proceedings, 1018, 15-20.

[26]   He, J.-H., Goldfain, E., Sigalotti, L.D. and Mejias, A. (2006) Beyond the 2006 Physics Nobel Prize for COBE: An Introduction to E-Infinity Spacetime Theory. China Science & Culture Publishing, Shanghai.

[27]   El Naschie, M.S. (2001) On a General Theory for Quantum Gravity. In: Diebner, H., Druckry, T. and Weibel, P., Eds., Science of the Interface, Genista Verlag, Tübingen, 52-57.

[28]   Duff, M. (1999) The World in Eleven Dimensions. IOP Publishing, Bristol.

[29]   Kaku, M. (2000) Strings, Conformal Fields and M-Theory. Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-0503-6

[30]   Amendola, L. and Tsujikawa, S. (2010) Dark Energy: Theory and Observations. Cambridge University Press, Cambridge.

[31]   Rindler, W. (2004) Relativity (Special, General and Cosmological). Oxford University Press, Oxford.

[32]   Halvorson, H. (2011) Deep Beauty—Understanding the Quantum World through Mathematical Innovation. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511976971

[33]   Ho, M.-W. (2014) E-Infinity Spacetime, Quantum Paradoxes and Quantum Gravity. Journal of the Institute of Science in Society, 62, 40-43.

[34]   El Naschie, M.S. (1998) Superstrings, Knots and Noncommutative Geometry in E-Infinity Space. International Journal of Theoretical Physics, 37, 2935-2951.
http://dx.doi.org/10.1023/A:1026679628582

[35]   El Naschie, M.S. (2006) Elementary Number Theory in Superstring Loop Quantum Mechanics, Twistors and E-Infinity High Energy Physics. Chaos, Solitons & Fractals, 27, 297-330.
http://dx.doi.org/10.1016/j.chaos.2005.04.116

[36]   El Naschie, M.S. (2004) Quantum Gravity, Clifford Algebra, Fuzzy Set Theory and the Fundamental Constants of Nature. Chaos, Solitons & Fractals, 20, 297-330.
http://dx.doi.org/10.1016/j.chaos.2003.09.029

[37]   El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646. http://dx.doi.org/10.1016/j.chaos.2008.09.059

[38]   El Naschie, M.S. (2009) Wild Topology, Hyperbolic Geometry and Fusion Algebra of High Energy Particle Physics. Chaos, Solitons & Fractals, 13, 1935-1945. http://dx.doi.org/10.1016/S0960-0779(01)00242-9

[39]   El Naschie, M.S. (2006) Hilbert, Fock and Cantorian Spaces in the Quantum Two-Slit Gedanken Experiment. Chaos, Solitons & Fractals, 27, 39-42. http://dx.doi.org/10.1016/j.chaos.2005.04.094

[40]   El Naschie, M.S. (1998) Penrose Universe and Cantorian Spacetime as a Model for Noncommutative Quantum Geometry. Chaos, Solitons & Fractals, 9, 931-933. http://dx.doi.org/10.1016/S0960-0779(98)00077-0

[41]   El Naschie, M.S. (2006) On an Eleven Dimensional E-Infinity Fractal Spacetime Theory. International Journal of Nonlinear Sciences & Numerical Simulation, 7, 407-409.

[42]   El Naschie, M.S. (2013) A Resolution of the Cosmic Dark Energy via Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3, 23-26. http://dx.doi.org/10.4236/jqis.2013.31006

[43]   El Naschie, M.S. (2006) Topics in the Mathematical Physics of E-Infinity Theory. Chaos, Solitons & Fractals, 30, 656-663. http://dx.doi.org/10.1016/j.chaos.2006.04.043

[44]   El Naschie, M.S. (2007) From Symmetry to Particles. Chaos, Solitons & Fractals, 32, 427-430.
http://dx.doi.org/10.1016/j.chaos.2006.09.016

[45]   Nottale, L. (2011) Scale Relativity and Fractal Space-Time. Imperial College Press, London.

[46]   El Naschie, M.S. (1994) Average Symmetry, Stability and Ergodicity of Multidimensional Cantor Sets. Il Nuovo Cimento B Series 11, 2, 149-157. http://dx.doi.org/10.1007/BF02727425

[47]   El Naschie, M.S. (1998) Fredholm Operator and the Wave-Particle Duality. Chaos, Solitons & Fractals, 9, 975-978.
http://dx.doi.org/10.1016/S0960-0779(98)00076-9

[48]   El Naschie, M.S. (2008) Symmetry Group Prerequisite for E-Infinity High Energy Physics. Chaos, Solitons & Fractals, 35, 975-978.

[49]   El Naschie, M.S. (2007) Hilbert Space, Poincaré Dodecahedron and Golden Mean Transfiniteness. Chaos, Solitons & Fractals, 31, 787-793. http://dx.doi.org/10.1016/j.chaos.2006.06.003

[50]   Neuenschwander, D. (2011) Emmy Noether’s Wonderful Theorem. The Johns Hopkins University Press, Baltimore.

[51]   Balachandran, A., Kurkcuoglu, S. and Vaidya, S. (2007) Lectures on Fuzzy and Fuzzy SUSY Physics. World Scientific, Singapore.

[52]   Finkelstein, D.R. (1996) Quantum Relativity. A Synthesis of the Ideas of Einstein and Heisenberg. Springer, Berlin.

[53]   El Naschie, M.S. (2014) On a New Elementary Particle from the Disintegration of the Symplectic 'tHooft-Veltman-Wilson Fractal Spacetime. World Journal of Nuclear Science and Technology, 4, 216-221.
http://dx.doi.org/10.4236/wjnst.2014.44027

[54]   El Naschie, M.S. (2014) From Modified Newtonian Gravity to Dark Energy via Quantum Entanglement. Journal of Applied Mathematics and Physics, 2, 803-806.

[55]   Tang, W., Li, Y., Kong, H.Y. and El Naschie, M.S. (2014) From Nonlocal Elasticity to Nonlocal Spacetime and Nanoscience. Bubbfil Nano Technology, 1, 3-12.

[56]   El Naschie, M.S. (2014) Cosmic Dark Energy Density from Classical Mechanics and Seemingly Redundant Riemannian Finitely Many Tensor Components of Einstein’s General Relativity. World Journal of Mechanics, 4, 153-156.
http://dx.doi.org/10.4236/wjm.2014.46017

[57]   El Naschie, M.S. (2014) Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and 'tHooft’s 4-ε Fractal Spacetime. American Journal of Astronomy & Astrophysics, 2, 34-37.

[58]   Auffray, J.-P. (2014) E-Infinity Dualities, Discontinuous Spacetimes, Xonic Quantum Physics and the Decisive Experiment.Journal of Modern Physics, 5, 1427-1436.

[59]   El Naschie, M.S. (2014) Electromagnetic—Pure Gravity Connection via Hardy’s Quantum Entanglement.Journal of Electromagnetic Analysis and Applications, 6, 233-237.

[60]   El Naschie, M.S. (2013) Topological-Geometrical and Physical Interpretation of the Dark Energy of the Cosmos as a “Halo” Energy of the Schrodinger Quantum Wave.Journal of Modern Physics, 4, 591-596.

[61]   Wigner, E.P. (1960) The Unreasonable Effectiveness of Mathematics in Natural Science. Communications in Pure and Applied Mathematics, 13, 1-14. http://dx.doi.org/10.1002/cpa.3160130102

[62]   Changeux, J. and Connes, A. (1989) Conversation on Mind, Matter and Mathematics. Princeton University Press, Princeton.

[63]   Helal, M.A., Marek-Crnjac, L. and He, J.-H. (2013) The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology. Open Journal of Microphysics, 3, 141-145.
http://dx.doi.org/10.4236/ojm.2013.34020

 
 
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