The Gap Labelling Integrated Density of States for a Quasi Crystal Universe Is Identical to the Observed 4.5 Percent Ordinary Energy Density of the Cosmos


Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy of the universe. Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals is identical to the previously measured and theoretically concluded ordinary energy density of the universe, namely a mere 4.5 percent of Einstein’s energy density, i.e. E(O) = mc2/22 where E is the energy, m is the mass and c is the speed of light. Consequently we conclude that the missing dark energy density must be E(D) = 1 - E(O) = mc2(21/22) in agreement with all known cosmological measurements and observations. This result could also be interpreted as a strong evidence for the self similarity of the geometry of spacetime, which is an expression of its basic fractal nature.

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El Naschie, M. (2014) The Gap Labelling Integrated Density of States for a Quasi Crystal Universe Is Identical to the Observed 4.5 Percent Ordinary Energy Density of the Cosmos. Natural Science, 6, 1259-1265. doi: 10.4236/ns.2014.616115.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Aoki, H. (Chairman) (2010) Condensed Matter Physics Meets High Energy Physics. IPMU, 1st International Conference, Tokyo, 8-12 February 2010.
[2] El Naschie, M.S. (1977) The Logic of Interdisciplinary Research. Chaos, Solitons & Fractals, 8, vi-x.
[3] Sachder, S. (2011) Quantum Phase Transition. 2nd Edition, Cambridge University Press, Cambridge.
[4] El Naschie, M.S. (2005) Experimental and Theoretical Arguments for the Number and the Mass of the Higgs Particle. Chaos, Solitons & Fractals, 23, 1091-1098.
[5] French, A. and Kennedy, P., Eds. (1985) Niels Bohr—A Centenary Volume. Harvard University Press, Cambridge-Mass.
[6] Baryshev, Y. and Teerikorpi, P. (2002) Discovery of Cosmic Fractals. World Scientific, Singapore.
[7] 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.
[8] Bellissard, J. (1992) Gap Labelling Theorems for Schrödinger’s Operators. In: Waldschmidt, M., et al., Eds., From Number Theory to Physics, Springer, Heidelberg, 538-630.
[9] Sze, S. (1981) Modern Physics of Semiconductors. John Wiley & Sons, New York.
[10] El Naschie, M.S. (1998) Fredholm Operator and the Wave-Particle Duality. Chaos, Solitons & Fractals, 9, 975-978.
[11] El Naschie, M.S. (1998) Penrose Universe and Cantorian Spacetime as a Model for Noncommutative Quantum Geometry. Chaos, Solitons & Fractals, 9, 931-933.
[12] Landi, G. (1997) An Introduction to Noncommutative Spaces and Their Geometrics. Springer, Berlin.
[13] El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Science, 3, 23-26.
[14] Corda, C. (2011) Cosmology of Einstein-Vlasov System in a Weak Modification of General Relativity. Modern Physics A, 26, 362-370.
[15] Corda, C. (2008) A Repulsive Force from a Modification of General Relativity. International Journal of Theoretical Physics, 47, 2679-2685.
[16] Tang, W., Li, Y., Kong, H.Y. and El Naschie, M.S. (2014) Nonlocal Elasticity to Nonlocal Spacetime and Nanoscience. Bubbfil Nanotechnology, 1, 3-12.
[17] El Naschie, M.S. (2014) From Modified Newtonian Gravity to Dark Energy via Quantum Entanglement. Journal of Applied Mathematics and Physics, 2, 803-806.
[18] He, J.H. (2014) A Tutorial Review on Fractal Spacetime and Fractional Calculus. International Journal of Theoretical Physics, 53, 3698-3718.
[19] Marek-Crnjac, L. and He, J.H. (2013) An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy. ?International Journal of Astronomy and Astrophysics, 3, 464-471.
[20] He, J.H. and Marek-Crnjac, L. (2013) The Quintessence of El Naschie’s Theory of Fractal Relativity and Dark Energy. Fractal Spacetime and Noncommutative Geometry in Quantum and High Energy Physics, 3, 130-137.
[21] 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.
[22] El Naschie, M.S. (2014) Compactified Dimensions as Produced by Quantum Entanglement, the Four Dimensionality of Einstein’s Smooth Spacetime and ‘tHooft’s 4-? Fractal Spacetime. American Journal of Astronomy & Astrophysics, 2, 34-37.
[23] 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.
[24] El Naschie, M.S. (2014) From Chern-Simon Holography and Scale Relativity to Dark Energy. Journal of Applied Mathematics and Physics, 2, 634-638.
[25] El Naschie, M.S. (2014) Why E Is Not Equal mc2. Journal of Modern Physics, 5, 743-750.
[26] Connes, A. (1994) Noncommutatie Geometry. Academic Press, San Diego.
[27] El Naschie, M.S. (2009) The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646.
[28] Auffray, J.P. (2014) E-Infinity Dualities, Discontinuous Spacetimes, Xonic Quantum Physics and the Decisive Experiment. Journal of Modern Physics, 5, 1427-1436.
[29] Hawking, S.W. and Ellis, G.F.R. (1973) The Large Scale Structure of Spacetime. Cambridge University Press, Cambridge.
[30] Karpenkov, O. (2013) Geometry of Continued Fractions. Springer, Berlin.
[31] Jacobsen, L., Ed. (1989) Analytic Theory of Continued Fractions. Lecture Notes No. 1406 in Mathematics. Springer, Berlin.
[32] Khanin, K., Dias, J.L. and Marklof, J. (2007) Multidimensional Continued Fractions, Dynamical Renormalization and KAM Theory. Communications in Mathematical Physics, 270, 197-231.
[33] El Naschie, M.S. (2013) A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light. International Journal of Modern Nonlinear Theory and Application, 2, 43-54.
[34] El Naschie, M.S. (2013) Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy. Journal of Modern Physics, 4, 1417-1428.
[35] 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.
[36] El Naschie, M.S. and Helal, A. (2013) Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography. International Journal of Astronomy and Astrophysics, 3, 318-343.
[37] El Naschie, M.S. (2000) Branching Polymers, Knot Theory and Cantorian Spacetime. Chaos, Solitons & Fractals, 11, 453-463.
[38] El Naschie, M.S. (1993) Penrose Tiling, Semi-Conduction and Cantorian l/fa Spectra in Four and Five Dimensions. Chaos, Solitons & Fractals, 3, 489-491.
[39] El Naschie, M.S. (1994) Forbidden Symmetries, Cantor Sets and Hypothetical Graphite. Chaos, Solitons & Fractals, 4, 2269-2272.
[40] Iovane, G., Laserra, E. and Tortoriello, F.S. (2004) Stochastic Self-Similar and Fractal Universe. Chaos, Solitons & Fractals, 20, 415-426.
[41] Ivanenko, D.D. and Gailuin, R.V. (1995) Quasicrystal Model of the Universe. (TpXVIIMexΔyHap.ceMnHapano ?n3.Bblaconx) (In Russian)
[42] Iovane, G. (2005) Mohamed El Naschie’s E-Infinity Cantorian Spacetime and Its Consequence in Cosmology. Chaos, Solitons & Fractals, 25, 775-779.
[43] Wolchover, N. (2014) Quasicrystal Meteorite Exposes Novel Processes in Early Solar System. Scientific American, 18 June, and Quanta Magazine.
[44] Murdzek, R. (2008) Hierarchical Cantor Set in the Large Scale Structure with Torus Geometry. Chaos, Solitons & Fractals, 38, 1269-1273.

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