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

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.

11 pages, proofread version to be published by Physical Review D

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• Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation
• The Barbero-Immirzi Parameter: An Enigmatic Parameter of Loop Quantum Gravity
• Quantization of time and the big bang via scale-invariant loop gravity
• Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame
• Bremsstrahlung of Light through Spontaneous Emission of Gravitational Waves