Model
Digital Document
Publisher
Florida Atlantic University
Description
We give a diffeomorphism and gauge covariant condition equivalent to homogeneity and
isotropy which can be quantized, yielding a definition of a diffeomorphism-invariant,
homogeneous isotropic sector of loop quantum gravity without fixing a graph. We then
specialize this condition to Bianchi I cosmologies, in which case it becomes a condition for
isotropy. We show how, by quantizing and imposing this condition in Bianchi I loop quantum
cosmology, one exactly recovers isotropic loop quantum cosmology, including the usual
‘improved dynamics.’ We will also discuss how this reduction sheds light on which operator
ordering to use when defining operators corresponding to directional Hubble rates, expansion,
and shear quantities relevant for discussing the resolution of the initial singularity.
isotropy which can be quantized, yielding a definition of a diffeomorphism-invariant,
homogeneous isotropic sector of loop quantum gravity without fixing a graph. We then
specialize this condition to Bianchi I cosmologies, in which case it becomes a condition for
isotropy. We show how, by quantizing and imposing this condition in Bianchi I loop quantum
cosmology, one exactly recovers isotropic loop quantum cosmology, including the usual
‘improved dynamics.’ We will also discuss how this reduction sheds light on which operator
ordering to use when defining operators corresponding to directional Hubble rates, expansion,
and shear quantities relevant for discussing the resolution of the initial singularity.
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