  Non-Riemannian generalization of the standard Born-Infeld (BI) Lagrangian is
introduced and analized from a theory of gravitation with dynamical torsion
field. The field equations derived from the proposed action lead to a trace
free gravitational equation (non-riemannian analog to the trace free equation
(TFE) from[1][2][3]) and the field equations for the torsion respectively. In
this theoretical context, the fundamental constants arise all from the same
geometry through geometrical invariant quantities (as from the curvature R).
New results involving generation of primordial magnetic fields and the link
with leptogenesis and baryogenesis are presented and possible explanations
given. The physically admisible matter fields can be introduced in the model
via the torsion vector h. Such fields include some dark matter candidates such
as axion, right neutrinos and Majorana and moreover, physical observables as
vorticity can be included in the same way. From a new wormhole soluton in a
cosmological spacetime with torsion we also show that the primordial cosmic
magnetic fields can originate from h? with the axion field (that is contained
in h) the responsible to control the dynamics and stability of the cosmic
magnetic field but not the magnetogenesis itself. The analisys of Grand Unified
Theories (GUT) in the context of this model indicates (as we have been pointed
out before) that the group manifold candidates are based in SO(10), SU(5) or
some exceptional groups as E(6),E (7), etc.
