Loop quantum cosmology

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As I understand it there have been different attempts to use LQG to make a theory of cosmology. The first one being done by Martin Bojowald and then later one being performed by Ashtekar, Pawloski and Singh. there is a description of what they did that was different but as a non cosmologist Im struggling to understand it. Is there anyone that can translate this into laymen terms?

"Roughly, at a key step in the procedure, the Hamiltonian constraint operator of [45] implicitly used a kinematic 3-metric ̊qab defined by the co-moving coordinates rather than the physical metric qab = a2̊qab (where a is the scale factor). When this is corrected, the new, improved Hamiltonian constraint again resolves the singularity and, at the same time, is free from all three drawbacks of the μo scheme."
from the following paper

https://arxiv.org/pdf/1108.0893.pdf
 

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