About non-Riemannian generalizations of Born-Infeld models and trace free gravitational equations

DIEGO JULIO CIRILO

Belgrado

Encuentro; 9th MATHEMATICAL PHYSICS MEETING: SCHOOL AND CONFERENCE ON MODERN MATHEMATICAL PHYSICS; 2017

s Institute of Physics, Belgrade

Non-Riemannian generalization of the standard Born-Infeld (BI)Lagrangian is reviewded in this talk from a theory of gravitation withdynamical torsion field. The field equations derived from the proposedaction lead to a trace free gravitational equation (non-riemanniananalog to the trace free equation (TFE) from[1][2][3]) and the fieldequations for the torsion respectively. In this theoretical context, thefundamental constants arise all from the same geometry through geometricalinvariant quantities (as from the curvature R). New resultsinvolving generation of primordial magnetic fields and the link withleptogenesis and baryogenesis are presented and possible explanationsgiven. The physically admisible matter fields can be introduced in themodel via the torsion vector h . Such fields include some dark mattercandidates such as axion, right neutrinos and Majorana and moreover,physical observables as vorticity can be included in the sameway. From a new wormhole soluton in a cosmological spacetime withtorsion we also show that the primordial cosmic magnetic fields canoriginate from h with the axion field (that is con tained in h ) the responsibleto control the dynamics and stability of the cosmic magneticfield but not the magnetogenesis itself. The analisys of Grand UnifiedTheories (GUT) in the context of this model indicates that the groupmanifold candidates are based in SO(10), SU(5) or some exceptionalgroups as E(6),E (7), etc. Hints about astrophysical consequences ofthis formulation are given