# Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity

## TL;DR

This paper explores a conformal loop quantum gravity approach to scalar-tensor gravity, proposing a way to treat the Immirzi parameter as a gauge choice through conformal transformations, potentially removing ambiguity.

## Contribution

It introduces a conformal Einstein frame in scalar-tensor gravity where the Immirzi parameter can be viewed as a gauge, unifying different values via conformal transformations.

## Key findings

- Immirzi parameter can be related by conformal transformations
- Loop quantization shares the same area gaps across frames
- Scalar field modulates the Immirzi parameter effects

## Abstract

Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. Here, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. In particular, we introduce a conformal Einstein frame in which loop quantization is implemented. We then discuss how different Immirzi parameters under this description may be related by conformal frame transformations and yet share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field.