Self-similar and oscillating solutions of Einsteinʹs equation and other relevant consequences of a stochastic self-similar and fractal Universe via El Naschieʹs ε(∞) Cantorian space–time

In this paper we make some suggestion regarding the unification of the fundamental forces and the age of the Universe in the context of the a stochastic self-similar and fractal Universe using El Naschieʹs ε(∞) Cantorian space–time. We also show how Einsteinʹs equation can admit for the scale factor a(t) a self-similar solution in agreement with our stochastic self-similar, fractal Universe and El Naschieʹs ε(∞) Cantorian space–time. In addition, this solution is found to be oscillating one. Thanks to the first quantization it is possible to recast the equations in a Schrödinger-like form. Consequently, the presently observed large scale structure reflects the phenomenology of the Early Universe or of the microscopic world. Again it appears clear that the Universe and the structures inside must have a memory of its quantum origin as conjectured sometime ago.