Accelerated expansion in a stochastic self-similar fractal universe

Abstract

In a recent paper, a cosmological model based on El Naschie E infinity cantorian spacetime was presented [1]. 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 it may be problematic to explain the present accelerated expansion of the Universe using the approach presented in [1]. As a better alternative we apply the same scaling law and a time-dependent gravitational constant, that follows from the observational constraints, to relativistic cosmology, i.e. the Friedmann's model. We are able to show that for a matterdominated 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 Ω Λ ≃ 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.2

Irreversible processes and a new model for the Universe

“…(2.1) is needed in order to clarify if it is a necessary extension from the viewpoint of El Naschie E-infinity theory [27][28][29][30][31], Iovane stochastic and self similar Universe [32][33][34][35], Nottale scale relativity [36][37][38][39] and Sidharth fractal Universe [40]. We note indeed that it is problematic to explain the present acceleration of the Universe as the effect of a model with an El Naschie E-infinity cantorian spacetime, a scaling law on Newtonian cosmology and a certain dependent gravitational constant G. On the contrary, if we use the fractal self-similarity of the G varying relativistic Friedmann model experimental data can be explained [41].…”