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.

Closing the gaps in quantum space and time: Conformally augmented gauge structure of gravitation

“…Although variables of the same form have previously appeared in Ref. [29], where they were derived in a specific ST theory excluding GR and matter coupling, here we have demonstrated the conformal Ashtekar-Barbero variables further arise from a large general class of gravity theories covering GR, ST, dilatonic gravity. In addition, we show that our formalism is preserved for matter coupling with SM-type theories.…”

“…For a single scalar field, Hamiltonian constraint (29) recovers the Hamiltonian constraint in Ref. [29]. The corresponding Hamiltonian density also takes the form of Eq.…”

“…Furthermore, instead of the more limited canonical formalism adopted in Ref. [29], the new conformal Holst principle in this work paves the way for a more covariant spinform models of the new conformal LQG to be developed.…”

“…Given their structures, it is clear from previous related studies that constraints C, G i , H a and H are first class [29,[31][32][33].…”

Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame

“…The holonomy correction in STT can be studied either in the Einstein frame or in the Jordan frame. In the Einstein frame, one first performs the conformal transformation to connection variable and then applies the polymer quantization of LQC to the transformed connection [15], while in the Jordan frame one directly quantizes the connection variable. For simplicity, the effects of holonomy correction in STT were mainly investigated in the Einstein frame in many particular models of STT over the past decade, such as the model with nonminimal coupling ξφ 2 [16,17], f (R) gravity and Brans-Dicke (BD) theory [18][19][20][21].…”