Geometrized Instantons and the Creation of the Universe

Abstract

A nonsingular cosmological scenario is presented in which the currently observed Riemannian configuration of spacetime originates from a primordial Weylian “stiff matter” phase driven by a geometrized inflaton-like field. In the particular case of a Friedman-Robertson-Walker line element, it is shown that an unstable original Minkowski vacuum starts to collapse adiabatically at a remote past and bounces when a minimum radius is attained. Throughout the collapsing stage, this matter-free Universe is accelerated (or “inflationary”). As in models of spontaneous quantum creation, the bouncing phase can be shown to correspond to the propagation of a Weyl instanton in an Euclideanized, classically forbidden region. In the course of the bouncing period, concurrent to the maximal deviation of the Riemannian configuration, a geometry-driven amplification mechanism operates causing the exponential increase of entropy and matter fluctuations. Once the environment temperature is always bounded, this nonadiabatical process stands for a “ Big — but finite — Bang” creation event, followed by a standard radiation-dominated era. The model describes an eternal, Friedman-like open Universe, free of many problems that hinder standard cosmology; the observed existence of a baryon excess also fits naturally within the proposed scheme.

Creation of cosmological magnetic fields in a bouncing cosmology

“…Let us briefly review these solutions. The EOM for gravitation plus scalar field written in conformal time are [32] …”

Extending the ADM formalism to Weyl geometry

“…This enables us to deduce the ADM Lagrangian for any Weyl-type gravity theory. Examples of the latter are a proposal known in the literature as the Weyl integrable spacetime gravity (WIST) [14,15], described by the action…”

Production of photons in a bouncing universe

“…As discussed in [33], there are nonsingular solutions in the theory of WIST that describe a FRW geometry plus a Weyl scalar field. Nonsingular solutions are also present in string theory [34].…”

“…Let us briefly review these solutions. The EOM for gravitation plus scalar field written in conformal time are [33] …”