Non-Riemannian geometry, Born-Infeld models and trace free gravitational equations

TL;DR

This paper introduces a non-Riemannian generalization of Born-Infeld gravity with torsion, deriving trace-free field equations, linking fundamental constants to geometry, and exploring implications for primordial magnetic fields, leptogenesis, and dark matter candidates.

Contribution

It presents a novel non-Riemannian Born-Infeld gravitational model with torsion, deriving trace-free equations and connecting fundamental constants to geometric invariants, with applications to cosmology and particle physics.

Findings

Derivation of trace-free gravitational equations from the model.

Generation of primordial magnetic fields linked to torsion and axions.

Potential connections to dark matter candidates and GUT groups.

Abstract

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.