Barbero-Immirzi field in canonical formalism of pure gravity

TL;DR

This paper promotes the Barbero-Immirzi parameter to a dynamic field within canonical gravity, revealing it as a pseudoscalar coupled to gravity, with implications for inflation and quantum gravity.

Contribution

It introduces a canonical formalism where the BI parameter is a field coupled via the Nieh-Yan invariant, offering a more natural framework than the Holst action.

Findings

BI field behaves as a canonical pseudoscalar

Framework suggests new avenues for inflation models

Implications for quantum gravity are discussed

Abstract

The Barbero-Immirzi (BI) parameter is promoted to a field and a canonical analysis is performed when it is coupled with a Nieh-Yan topological invariant. It is shown that, in the effective theory, the BI field is a canonical pseudoscalar minimally coupled with gravity. This framework is argued to be more natural than the one of the usual Holst action. Potential consequences in relation with inflation and the quantum theory are briefly discussed.