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Accelerated expansion in a stochastic self-similar fractal universe

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  • Santini, Eduardo Sergio
  • Lemarchand, Guillermo Andrés

Abstract

In a recent paper, a cosmological model based on El Naschie E infinity Cantorian space–time was presented [Iovane G. Varying G, accelerating universe, and other relevant consequences of a stochastic self-similar and fractal universe. Chaos, Solitons & Fractals 2004;20:657–67]. In that work, it was claimed that the present accelerated expansion of the universe can be obtained as the effect of a scaling law on Newtonian cosmology with a certain time-dependent gravitational constant (G). In the present work we show that such a cosmological model actually describes a decelerated universe. Then starting from the scenario presented in that paper, we realize a complementary approach based on an extended Friedmann model. In fact, we apply the same scaling law and a time-dependent gravitational constant, that follows from the observational constraints, to relativistic cosmology, i.e. a (extended) Friedmann’s model. We are able to show that for a matter-dominated flat universe, with the scaling law and a varying G, an accelerated expansion emerges in such a way that the function luminosity distance vs redshift can be made close to the corresponding function that comes from the usual Friedmann’s model supplemented with a cosmological constant, of value ΩΛ≃0.7. Then the measurements of high redshift supernovae, could be interpreted as a consequence of the fractal self-similarity of the G varying relativistic universe.

Suggested Citation

  • Santini, Eduardo Sergio & Lemarchand, Guillermo Andrés, 2006. "Accelerated expansion in a stochastic self-similar fractal universe," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1099-1105.
  • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:1099-1105
    DOI: 10.1016/j.chaos.2005.08.017
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    References listed on IDEAS

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    1. Kelvin K. S. Wu & Ofer Lahav & Martin J. Rees, 1999. "The large-scale smoothness of the Universe," Nature, Nature, vol. 397(6716), pages 225-230, January.
    2. Iovane, G., 2006. "Cantorian space–time, Fantappie’s final group, accelerated universe and other consequences," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 618-629.
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    Cited by:

    1. Sadeghi, J. & Saadat, H. & Pourhassan, B., 2009. "Relation between dark matter density and temperature with power law," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1080-1083.

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