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Waveguiding and mirroring effects in stochastic self-similar and Cantorian $${\mathcal E}^{(\infty)}$$ universe. (English) Zbl 1070.83542
Summary: A waveguiding effect is considered with respect to the large scale structure of the Universe, where the structures formation appears as if it were a classically self-similar random process at all astrophysical scales. The result is that it seems we live in an El Naschie’s $${\mathcal E}^{(\infty)}$$ Cantorian space-time, where gravitational lensing and waveguiding effects can explain the appearing Universe. In particular, we consider filamentary and planar large scale structures as possible refraction channels for electromagnetic radiation coming from cosmological structures. From this vision the Universe appears like a large self-similar adaptive mirrors set. Consequently, an infinite Universe is just an optical illusion that is produced by mirroring effects connected with the large scale structure of a finite and not so large Universe. Thanks to the presented analytical model supported by a numerical simulation, it is possible to explain the quasar luminosity distribution and the presence of “twin” or “brother” objects. More generally, the infinity and the abundance of astrophysical objects could be just a mirroring effect due to the peculiar self-similarity of the Universe.

##### MSC:
 83F05 Relativistic cosmology 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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