Non-Riemannian generalization of the standard Born–Infeld (BI) Lagrangian is introduced and analyzed 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 Finkelstein et al., 2001, Ellis et al., 2011, Ellis, 2014) 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 admissible matter fields can be introduced in the model via the torsion vector $h_{\mu }$. 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 solution in a cosmological spacetime with torsion we also show that the primordial cosmic magnetic fields can originate from $h_{\mu }$ with the axion field (that is contained in $h_{\mu }$) the responsible to control the dynamics and stability of the cosmic magnetic field but not the magnetogenesis itself. As we pointed out before (Cirilo-Lombardo, 2017), the analysis 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 $E(6)$, $E\left(7\right)$, etc.

介绍了标准Born-Infeld（BI）拉格朗日算子的非黎曼概化，并从具有动态扭转场的引力理论进行了分析。从拟议的行动中得出的场方程导致了无痕引力方程（Finkelstein等人，2001； Ellis等人，2011； Ellis，2014）的无痕迹引力方程的非黎曼模拟（TFE）。扭转方程。在此理论上下文中，基本常数全部来自相同的几何形状，并具有几何不变量（例如曲率R）。提出了涉及原始磁场产生以及与瘦素形成和重生的联系的新结果，并给出了可能的解释。可以通过扭转矢量将物理上可允许的物质场引入模型中$H_{\mu }$。这些场包括一些暗物质候选物，例如轴突，右中微子和马约拉纳，此外，由于可以以相同的方式包含涡度，因此可以观察到物理观测结果。从宇宙时空中带有扭力的新虫洞解中，我们还表明原始宇宙磁场可以源自$H_{\mu }$ 与轴力场（包含在 $H_{\mu }$）负责控制宇宙磁场的动力学和稳定性，但不能控制磁化作用本身。正如我们之前指出的那样（Cirilo-Lombardo，2017），在该模型的背景下对大统一理论（GUT）的分析表明，该组流形候选基于$\mathrm{小号}Ø（10）$， $\mathrm{小号}ü（5）$ 或一些特殊群体 $Ë（6）$， $Ë（7）$等