Dirac fields, torsion and Barbero-Immirzi parameter in Cosmology

TL;DR

This paper explores how Dirac fields coupled with torsion and the Barbero-Immirzi parameter influence cosmological evolution, revealing that the resulting effective fluid can drive inflation or behave as ultra-hard matter depending on fermion mass.

Contribution

It demonstrates the equivalence of the BI parameter's effects to a perfect fluid in the zero-mass limit and analyzes the resulting cosmological phases driven by fermion mass and torsion.

Findings

Massless fermions lead to a stiff fluid with w=1, independent of BI parameter.

Finite fermion mass induces variable w, causing inflation or ultra-hard states.

Late universe approaches pressureless fluid with w=0.

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 $m\to\infty$).