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

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 Weyls 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 inflatons 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.