Origin of time before inflation from a topological phase transition

MAURICIO BELLINI

PHYSICS OF THE DARK UNIVERSE

Elsevier

Lugar: Amsterdam; Año: 2017 vol. 17 p. 22 - 24

We study the origin of the universe (or pre-inflation) by suggesting that the primordial space-time in the universe suffered a global topological phase transition, from a4D Euclidean manifold to an asymptotic 4D hyperbolic one. We introduce a complex time, $au$, such that its real part becomes dominant after started the topological phase transition. Before the big bang, $au$ is a space-like coordinate, so that can be considered as a reversal variable. After the phase transition is converted in a causal variable. The formalism solves in a natural manner the quantum to classical transition of the geometrical relativistic quantum fluctuations: $sigma$, which has a geometric origin.