Cosmic Dark Energy Density from Classical Mechanics and Seemingly Redundant Riemannian Finitely Many Tensor Components of Einstein’s General Relativity

Mohamed El Naschie

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

DOI: 10.4236/wjm.2014.46017                

Abstract

We determine the limit of the ratio formed by the independent components of the Riemann tensor to the non-zero component as space dimensionality tends to infinity and find it to be 12. Subsequently we use this result in conjunction with Newtonian classical mechanics to show that the ordinary measurable cosmic energy density is given by while the dark energy density is obviously the Legendre transformation dual energy E(D) = 1 - E(O). The result is in complete agreement with the COBE, WMAP and type 1a supernova measurements.

Keywords

Semi Classical Quantum Systems, Dark Energy, Accelerated Cosmic Expansion, Riemannian Tensor, Infinite Dimensional Topology, Nonlocal Elasticity

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Martin, J.L. (1995) General Relativity. Prentice Hall, London. in particular pages 89 and 111.
[2]	Linder, E. (2008) Dark Energy. Scholarpedia, 3, 4900. http://dx.doi.org/10.4249/scholarpedia.4900
[3]	Caroll, S. (2013) Why Does Dark Energy Make the Universe Accelerate? http://www.preposterousuniverse.com/blog/2013/ 11/16/why-does-dark-energy-make-t
[4]	El Naschie, M.S. (2014) Calculating the Exact Experimental Density of the Dark Energy in the Cosmos Assuming a Fractal Speed of Light. International Journal of Modern Nonlinear Theory and Application. in press.
[5]	El Naschie, M.S. (2014) Cosserat-Cartan and de Sitter-Witten Spacetime Setting for Dark Energy. Quantum Matter. in press.
[6]	El Naschie, M.S. (2014) Pinched Material Einstein Spacetime Produces Accelerated Cosmic Expansion. International Journal of Astronomy and Astrophysics, 4, 80-90. http://dx.doi.org/10.4236/ijaa.2014.41009
[7]	El Naschie, M.S. (2013) The Quantum Gravity Immirzi Parameter—A General Physical and Topological in Terpretation. Gravitation and Cosmology, 19, 151-155. http://dx.doi.org/10.1134/S0202289313030031
[8]	El Naschie, M.S. (2014) Dark energy via Quantum Field Theory in Curved Spacetime. Journal of Modern Physics and Applications, 2, 1-7.
[9]	El Naschie, M.S. (2013) Experimentally Based Theoretical Arguments that Unruh’s Temperature, Hawking’s Vacuum Fluctuation and Rindler’s Wedge Are Physically Real. American Journal of Modern Physics, 2, 357-361. http://dx.doi.org/10.11648/j.ajmp.20130206.23
[10]	El Naschie, M.S. (2013) Quantum Entanglement: Where Dark Energy and Negative Gravity Plus Accelerated Expansion of the Universe Comes from. Journal of Quantum Information Science, 3, 57-77. http://dx.doi.org/10.4236/jqis.2013.32011
[11]	Eringen, A.C. and Edelen, D.G. (1972) On Nonlocal Elasticity. International Journal of Engineering Science, 10, 233-248. http://dx.doi.org/10.1016/0020-7225(72)90039-0
[12]	Challamel, N., Wang, C.M. and Elishakoff, I. (2014) Discrete Systems Behave as Nonlocal Structural Elements; Bending Buckling and Vibration Analysis. European Journal of Mechanics—A/Solids, 44, 125-135. http://dx.doi.org/10.1016/j.euromechsol.2013.10.007
[13]	El Naschie, M.S. (1990) Stress, Stability and Chaos in Structural Engineering: An Energy Approach. McGraw Hill, London.
[14]	El Naschie, M.S. (2014) The Meta Energy of Dark Energy. Open Journal of Philosophy. In press.