The geometrical nature of the cosmological inflation in the framework of the Weyl-Dirac conformal gravity theory

TL;DR

This paper explores the geometric origins of the inflaton field within Weyl-Dirac conformal gravity, linking inflationary dynamics to fundamental geometric concepts and potential quantum phenomena.

Contribution

It demonstrates how the inflaton can be derived from Weyl's differential geometry and connects inflationary symmetry changes to the Weyl curvature scalar.

Findings

Inflaton field rooted in Weyl geometry

Symmetry transition from Weylan to Riemannian during inflation

Weyl curvature scalar relates to quantum phenomenology

Abstract

The nature of the scalar field responsible for the cosmological inflation, the \qo{inflaton}, is found to be rooted in the most fundamental concept of the Weyl's differential geometry: the parallel displacement of vectors in curved space-time. The Euler-Lagrange theory based on a scalar-tensor Weyl-Dirac Lagrangian leads straightforwardly to the Einstein equation admitting as a source the characteristic energy-momentum tensor of the inflaton field. Within the dynamics of the inflation, e.g. in the slow roll transition from a \qo{false} toward a \qo{true vacuum}, the inflaton's geometry implies a temperature driven symmetry change between a highly symmetrical \qo{Weylan} to a low symmetry \qo{Riemannian} scenario. Since the dynamics of the Weyl curvature scalar, constructed over differentials of the inflaton field, has been found to account for the quantum phenomenology at the microscopic scale, the present work suggests interesting connections between the \qo{micro} and the \qo{macro} aspects of our Universe.