Abstract

The article claims that the nature of the scalar field responsible for cosmological inflation is rooted in the most fundamental concepts of Hermann Weyl’s Conformal Differential Geometry. Within a cosmological context the Euler-Lagrange theory based on a scalartensor Lagrangian, similar to the one already adopted by C.Brans and R.H.Dicke, leads via an extended and complete variational procedure, to a complete Einstein equation admitting an energy-momentum tensor accounting for the essential geometrical background as a source. In the article, the integrable Weyl theory applied to the dynamics of a relativistic fluid shows a hitherto never explained “negative pressure” condition responsible for the scale-acceleration of the dynamical expansion of the Universe. As a significant example, the case of a spherically symmetrical star filled with a fluid of constant mass density is also discussed. The dynamics of the curvature constructed over the differentials of this geometrical scalar field, here identified by “scalar Weyl potential” φ( x) is found to account for various critical aspects of the overall quantum phenomenology. A model for dark matter and dark energy, based on the sound hypotesis of a gravity induced de-localization of the zero-point vacuum energy is also presented and discussed in the article, showing the possibility of detection of the dark-fields by advanced Gravitational Wave (GW) techniques. An extension of the conformal theory to relevant local and nonlocal quantum processes is also briefly included. Finally, an extended comment by Gerhard t’Hooft about the absolute relevance of the Conformal Symmetry, as a “missing symmetry component for space-time”, is reproduced and discussed in the context of our theoretical perspective and of the inner significance of the methods and results expressed in the article.

Keywords

cosmological inflation