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
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.
