Interaction of the Barbero--Immirzi Field with Matter and Pseudo-Scalar Perturbations

Abstract

In Loop Quantum Gravity the classical point of departure is the Einstein-Hilbert action modified by the addition of the so-called Holst term. Classically, this term does not affect the equations of motion, but it induces a well-known quantization ambiguity in the quantum theory, parametrized by the Barbero--Immirzi parameter. Recently, it has been suggested to promote the Barbero--Immirzi parameter to a field. The resulting theory, obtainable starting from the usual Holst action, is General Relativity coupled to a pseudo-scalar field. However, this theory turns out to have an unconventional kinetic term for the BI field and a rather unnatural coupling with fermions. The main goal of this work is twofold: Firstly, to propose a further generalization of the Holst action, which yields a theory of gravity and matter with a more natural coupling to the Barbero--Immirzi field; secondly, to study the possible implications for cosmology correlated to the existence of this new pseudo-scalar field.

V1: 13 pages. V2: 18 pages, 2 Sections added, references added, presentation improved. V3: minor corrections, version accepted for publication in PRD

References in corpus (11)

• The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?
• Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity
• A gravitational-wave probe of effective quantum gravity
• Barbero-Immirzi field in canonical formalism of pure gravity
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• Topological Interpretation of Barbero-Immirzi Parameter
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• Chern-Simons Modified Gravity as a Torsion Theory and its Interaction with Fermions
• Remarks on Barbero-Immirzi parameter as a field
• Holst Actions for Supergravity Theories
• Fermions in Loop Quantum Cosmology and the Role of Parity

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• Gauge invariant coupling of fields to torsion: a string inspired model