Teoria de Einstein-Cartan com campos de Dirac, ação de Holst e fluido de spin

Abstract

In this work we present the Einstein-Cartan theory by means of Holst action with Dirac fields description minimally coupled to curvature and torsion. The coupling term four-fermion emerges after using the relationship between the torsion and source of matter, previously calculated by Perez and Rovelli. The coupling constant is related to the Barbero-Immirzi (BI) parameter, which emerges from the Holst action. We investigate cosmological solutions in the standard Friedman-Lemaître-Robertson-Walker (FLRW) model. Whe show in the massless case that the equation of state describes a perfect fluid with p = wρ, with w = 1. For the massive case, is possible to describe an inflationary phase with w = 1 for early universe. We study also the coupling between fermions and gravitation with torsion in the presence of spin fluid (Weyssenhofffluid),andweshowtheequivalentactionwithfour-fermioninteraction,atermof self-interaction of the spin fluid and a interaction term between fermionic field and spin fluid. In all these cases, there is the dependence on BI parameter. The interaction term between the fermioniccurrentandthespintensorcanbeconsideredasanewstartingframeworkforstuding cosmological effects.