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

DIEGO JULIO CIRILO

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2017

0219-8878

Theory of gravitation based on a non-Riemannian geometry with dynamical torsion fieldis geometrically analyzed. To this end, the simplest Lagrangian density is introduced asa 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 thestandard Born?Infeld (BI) Lagrangian. As soon as the functional action is rewrittenin the BI form, the dynamical equations lead the trace-free GR-type equation and thefield equations for the torsion, respectively: both equations emerge from the model ina sharp contrast with other attempts where additional assumptions were heuristicallyintroduced. In this theoretical context, the Einstein κ, Newton G and the analog to theabsolute b-field into the standard BI theory all arise from the same geometry throughgeometrical invariant quantities (as from the curvature R). They can be clearly identifiedand correctly interpreted both physical and geometrically. Interesting theoreticaland physical aspects of the proposed theory are given as clear examples that show theviability of this approach to explain several problems of actual interest. Some of themare the dynamo effect and geometrical origin of αΩ term, origin of primordial magneticfields and the role of the torsion in the actual symmetry of the standard model. Therelation with gauge theories, conserved currents, and other problems of astrophysicalcharacter is discussed with some detail.