Generalized Ashtekar variables for Palatini f(R) models

TL;DR

This paper develops a new set of Ashtekar variables for Palatini f(R) gravity models, incorporating torsion and scalar fields, to preserve SU(2) gauge symmetry and explore quantum geometric effects.

Contribution

It introduces a novel formulation of Ashtekar variables for Palatini f(R) models with torsion and scalar fields, extending Loop Quantum Gravity techniques.

Findings

Constructed a new Gauss constraint for Palatini f(R) models with torsion.

Analyzed the scalar field's dynamical role influenced by the Immirzi parameter.

Compared metric and Palatini approaches, highlighting differences in the Hamiltonian.

Abstract

We consider special classes of Palatini f(R) theories, featured by additional Loop Quantum Gravity inspired terms, with the aim of identifying a set of modified Ashtekar canonical variables, which still preserve the SU(2) gauge structure of the standard theory. In particular, we allow for affine connection to be endowed with torsion, which turns out to depend on the additional scalar degree affecting Palatini f(R) gravity, and in this respect we successfully construct a novel Gauss constraint. We analyze the role of the additional scalar field, outlining as it acquires a dynamical character by virtue of a non vanishing Immirzi parameter, and we describe some possible effects on the area operator stemming from such a revised theoretical framework. Finally, we compare our results with earlier studies in literature, discussing differences between metric and Palatini approaches. It is worth noting how the Hamiltonian turns out to be different in the two cases. The results can be reconciled when the analysis is performed in the Einstein frame.