Dirac fields, torsion and Barbero-Immirzi parameter in Cosmology

Abstract

We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state \ $p=w\rho$, with $w=1$ which is independent of the BI parameter. The existence of mass imposes a variable $w$, which creates either an inflationary phase with $w=-1$, or assumes an ultra hard equation of states $w=1$ for very early universe. Both phases relax to a pressure less fluid $w=0$ for late universe (corresponding to the limit $m\to \infty$).

LaTeX file (with jcappub.sty), 16 pages, no figures. Some formulations and discussions slightly modified, fits the version to be published in JCAP

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