  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. As a necessary consequence, the
diffeomorphism constraint picks up non-perturbative quantum corrections thus
hinting at a modification of the underlying space-time structure, a novel
ingredient compared to the usual treatment of (spatial) diffeomorphisms in LQG.
This work extends a similar result obtained in the context of spherically
symmetric gravity coupled to a scalar field, suggesting that self dual
variables could be better suited than their real counterparts to treat
inhomogeneous LQG models.
