Remarks on Barbero-Immirzi parameter as a field

TL;DR

This paper analyzes a modified gravity theory with a propagating torsion field, extending previous scalar-tensor equivalence to include fermions and exploring potential inflationary implications.

Contribution

It extends the scalar field equivalence in torsion gravity to fermionic matter and introduces a potential for the scalar, opening new avenues for cosmological applications.

Findings

The theory has second order equations with no free coupling constants.

It includes an effective interaction between the scalar field and fermionic currents.

A potential for the scalar field may allow interpretation as an inflaton.

Abstract

We revisit a propagating torsion gravity theory obtained by introducing a field coupled to the Holst term in the first-order Einstein-Cartan action. The resulting theory has second order field equations, no adjustable coupling constants, and one more propagating degree of freedom as compared to general relativity. When no fermions are present the theory is known to be equivalent to that of a single massless scalar field canonically coupled to gravity. We extend this result to the case with fermions and obtain an effective interaction between the scalar field and the fermionic currents. We also describe a version of the theory with a potential for the scalar field and discuss whether it can be interpreted as the inflaton.