A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables

Understand

Scalar cosmological perturbations in loop quantum cosmology (LQC) is revisited in a covariant manner, using self dual Ashtekar variables.

• For real-valued Ashtekar-Barbero variables, this `deformed algebra' approach has been shown to implement holonomy corrections from loop quantum gravity (LQG) in a consistent manner, albeit deforming the algebra of modified constraints in the process.
• This deformation has serious conceptual ramifications, not the least of them being an effective `signature-change' in the deep quantum regime.
• In this paper, we show that working with self dual variables lead to an undeformed algebra of hypersurface deformations, even after including holonomy corrections in the effective constraints.