A Topological Magueijo-Smolin Varying Speed of Light Theory, the Accelerated Cosmic Expansion and the Dark Energy of Pure Gravity


The paper presents a detailed analysis of ordinary and dark energy density of the cosmos based on two different but complimentary theories. First, and starting from the concept of the speed of light being an average over multi-fractals, we use Magueijo-Smolin’s ingenious revision of Einstein’s special relativity famous formula E = mc2 to a doubly special formula which includes the Planck energy as invariant to derive the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) wheremis the mass andcis the speed of light. Second we use the topological theory of pure gravity to reach the same result thus confirming the correctness of the theory of varying speed of light as well as the COBE, WMAP and Type 1a supernova cosmological measurements.

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Naschie, M. , Marek-Crnjac, L. , Helal, M. and He, J. (2014) A Topological Magueijo-Smolin Varying Speed of Light Theory, the Accelerated Cosmic Expansion and the Dark Energy of Pure Gravity. Applied Mathematics, 5, 1780-1790. doi: 10.4236/am.2014.512171.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Amendola, L. and Tsujikawa, S. (2010) Dark Energy: Theory and Observations. Cambridge University Press, Cambridge.
[2] Baryshev, Y. and Teerikorpi, P. (2002) Discovery of Cosmic Fractals. World Scientific, Singapore.
[3] Nottale, L. (2011) Scale Relativity. Imperial College Press, London.
[4] Ord, G. (1983) Fractal Space-Time. A geometric Analogue of Relativistic Quantum Mechanics. Journal of Physics A: Mathematical and General, 16, 1869.
[5] El Naschie, M.S. (2011) Quantum Entanglement as a Consequence of a Cantorian Micro Space-Time Geometry. Journal of Quantum Information Science, 1, 50-53.
[6] He, J.-H., et al. (2011) Quantum Golden Mean Entanglement Test as the Signature of the Fractality of Micro Space-Time. Nonlinear Science Letters B, 1, 45-50.
[7] El Naschie, M.S. (2009) The Theory of Cantorian Space-Time and High Energy Particle Physics (An Informal Review). Chaos, Solitons & Fractals, 41, 2635-2646.
[8] El Naschie, M.S. (2004) A Review of E-Infinity Theory and the Mass Spectrum of High Energy Particle Physics. Chaos, Solitons & Fractals, 19, 209-236.
[9] Mageuijo, J. and Smolin, L. (2001) Lorentz Invariance with an Invariant Energy Scale. arXiv: hep-th/0112090V2.
[10] Mageuijo, J. (2003) Faster Than the Speed of Light. William Heinemann, London.
[11] El Naschie, M. S. (2006) On an Eleven Dimensional E-Infinity Fractal Space-Time Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 407-409.
[12] El Naschie, M. S. (2006) The “Discrete” Charm of Certain Eleven Dimensional Space-Time Theory. International Journal of Nonlinear Sciences and Numerical Simulation, 7, 477-481.
[13] Duff, M. (1999) The World in Eleven Dimensions. IOP Publishing Ltd., Bristol.
[14] Yau, S. T. and Nadis, S. (2010) The Shape of Inner Space. Basic Book, Persons Group, New York.
[15] Randal, L. (2005) Warped Passages. Allen Lane-Penguin Books, London.
[16] Penrose, R. (2004) The Road to Reality. Jonathan Cape, London.
[17] Becker, K., Becker, M. and Schwarz, J. (2007) String Theory and M-Theory. Cambridge University Press, Cambridge.
[18] Schwarz, P.M. and Schwarz, J.H. (2004) Special Relativity from Einstein to Strings. Cambridge University Press, Cambridge.
[19] Hardy, L. (1993) Non-Locality of Two Particles without Inequalities for Almost All Entangled States. Physical Review Letters, 71, 1665-1668.
[20] Bengtsson, I. and Zyczkowski, K. (2008) Geometry of Quantum States. Cambridge University Press, Cambridge.
[21] Nakajima, S. and Murayama, Y. (Eds.) (1996) Foundations of Quantum Mechanics in the Light of New Technologies. World Scientific, Singapore.
[22] Braginsky, V. and Vyatchanin, S.P. (1981) Dokl. Akad. Nauk SSSR, 259, 570 [Sov. Phys. Dokl., 27, (1982), 478].
[23] He, J.H. and El Naschie, M.S. (2012) On the Monadic Nature of Quantum Gravity as Highly Structured Golden Ring Spaces and Spectra. Fractal Space-Time and Non-Commutative Geometry in Quantum and High Energy Physics, 3, 94-98, Asian Academic Publisher Limited, Hong Kong.
[24] El Naschie, M.S. (2013) A Resolution of Cosmic Dark Energy via a Quantum Entanglement Relativity Theory. Journal of Quantum Information Since, 3, 23-26.
[25] Marek-Crnjac, L., He, J.H. and El Naschie, M.S. (2013) Chaotic Fractals at the Root of Relativistic Quantum Physics and Cosmology. International Journal of Modern Nonlinear Theory and Application, 2, 78-88.
[26] El Naschie, M.S. (2013) A Rindler-KAM Space-Time Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy. International Journal of Astronomy and Astrophysics, 3, 483-493.
[27] El Naschie, M.S. (2013) From Yang-Mills Photon in Curved Space-Time to Dark Energy Density. Journal of Quantum Information Science, 3, 121-126.
[28] Kheyfets, A. and Wheeler, J.A. (1986) Boundary of a Boundary Principle and Geometric Structure of Field Theories. International Journal of Theoretical Physics, 25, 573-580.
[29] Hartle, J.P. (1983) Wave Function of the Universe. Physical Review D, 28, 2960.
[30] Marek-Crnjac, L. (2013) Cantorian Space-Time Theory—The Physics of Empty Sets in Connection with Quantum Entanglement and Dark Energy. Lambert Academic Publishing, Saarbrücken.

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