Some Thoughts Concerning Spacetime Models in Cosmology : Role of Gravitation and Electromagnetism
Résumé
Considering an Einstein-Cartan vacuum spacetime, this work focusses on the influence of electromagnetic field on the accelerated expansion of the universe. In addition to metric and torsion, we study the influence of the compatibility of both of them with the volume-form, needed to correctly define any Lagrangian of the vacuum. The action including Einstein-Palatini and Yang-Mills Lagrangians is considered. Application of Variation Procedure allows us to derive fields equations : (1) Maxwell, (2) Einstein-Maxwell and (3) a new linking relation giving what we called distortion of the spacetime. This (third-order) distorsion tensor is expressed explicitly and is generated by a particular component of the electromagnetic field : the Chern-Simmons current which is constituted by Magnetic Helicity and Spin Angular Momentum of the wave. It is deduced that norm of the torsion-vector acts as either dark energy (spacelike torsion) or dark matter (timelike torsion) depending its sign. The integral curves of the torsion-vector field might be suggested as the tangent field of gigantic filaments, and confirming that the two major forces remain the gravitation and magnetic forces.
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