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M. Crasmareanu and C. Hretcanu, “Golden Differential Geometry,” Chaos, Solitons & Fractals, Vol. 38, No. 5, 2008, pp. 1229-1238. doi:10.1016/j.chaos.2008.04.007

has been cited by the following article:

• TITLE: The Missing Dark Energy of the Cosmos from Light Cone Topological Velocity and Scaling of the Planck Scale

  AUTHORS: Mohamed S. El Naschie

  KEYWORDS: Scaling the Planck Scale; Weyl Scaling; Nottale Scaling; Dark Energy; Quantum Relativity

  JOURNAL NAME: Open Journal of Microphysics, Vol.3 No.3, August 12, 2013

  ABSTRACT: The paper presents an exact analysis leading to an accurate theoretical prediction of the amount of the mysteriously missing hypothetical dark energy density in the cosmos. The value found, namely 95.4915028% is in full agreement with earlier analysis, the WMAP and the supernova cosmic measurements. The work follows first the strategy of finding a critical point which separates a semi-classical regime from a fully relativistic domain given by topological unit interval velocity parameter then proceeds to wider aspects of a topological quantum field of fractal unit interval. This idea of a critical velocity parameter was first advanced by Sigalotti and Mejias in 2006 who proposed a critical value equal . A second interesting proposal made in 2012 by Hendi and Sharifzadeh set the critical point at 0.8256645. The present analysis is based upon a light cone velocity quantized coordinate. This leads to the same quantum relativity energy mass relation found in earlier publications by rescaling that of Einstein’s special relativity. Two effective quantum gravity formulae are obtained. The first is for the ordinary measurable energy of the quantum particle while the second is for dark energy density of the quantum wave which we cannot measure directly and we can only infer its existence from the measured accelerated expansion of the universe E(D) = where . The critical velocity parameter in this case arises naturally to be . The results so obtained are validated using a heuristic Lorentzian transformation. Finally the entire methodology is put into the wider perspective of a fundamental scaling theory for the Planck scale proposed by G. Gross.