Abstract:

Non-Riemannian generalization of the standard Born-Infeld (BI) Lagrangian is reviewded in this talk 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 more-over, 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 con tained 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 that the group manifold candidates are based in SO(10), SU(5) or some exceptional groups as E(6),E (7), etc. Hints about astrophysical consequences of this formulation are given. © 2017 Proceedings of the 9th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics. All rights reserved.