Nothing into Something and Vice Versa: A Cosmological Scenario

Abstract

In the almost empty universe (with almost no matter in it), stochastic gravitational waves (SGW) of finite amplitude produce a de Sitter regime as a solution, which is invariant with respect to the Wick rotation. Asymptotically, super horizon SGWs do not “feel” difference between Lorentzian and Euclidean spacetime and belong simultaneously to both of them. The universe is finishing its evolution in Euclidean spacetime, i.e., it disappears into nothing. Quantum fluctuations of the gravitational field (gravitons) produce a de Sitter regime again in Euclidean spacetime where the current universe finished its existence, and due to the invariance of the de Sitter regime with respect to Wick rotation, the next universe starts its life with de Sitter inflation in Lorentzian spacetime. Such a scenario assumes that a permanent process of birth, death and rebirth of an infinite sequence of universes takes place on an infinite time axis.