Non-Riemannian generalizations of the Born–Infeld model and the meaning of the cosmological term

Abstract

Theory of gravitation based on a non-Riemannian geometry with dynamical torsion field is geometrically analyzed. To this end, the simplest Lagrangian density is introduced as a measure (reminiscent of a sigma model) and the dynamical equations are derived. Our goal is to rewrite this generalized affine action in a suitable form similar to the standard Born–Infeld (BI) Lagrangian. As soon as the functional action is rewritten in the BI form, the dynamical equations lead the trace-free GR-type equation and the field equations for the torsion, respectively: both equations emerge from the model in a sharp contrast with other attempts where additional assumptions were heuristically introduced. In this theoretical context, the Einstein [Formula: see text], Newton [Formula: see text] and the analog to the absolute [Formula: see text]-field into the standard BI theory all arise from the same geometry through geometrical invariant quantities (as from the curvature [Formula: see text]). They can be clearly identified and correctly interpreted both physical and geometrically. Interesting theoretical and physical aspects of the proposed theory are given as clear examples that show the viability of this approach to explain several problems of actual interest. Some of them are the dynamo effect and geometrical origin of [Formula: see text] term, origin of primordial magnetic fields and the role of the torsion in the actual symmetry of the standard model. The relation with gauge theories, conserved currents, and other problems of astrophysical character is discussed with some detail.