Quantum cosmology of (loop) quantum gravity condensates: An example
  Spatially homogeneous universes can be described in (loop) quantum gravity as
condensates of elementary excitations of space. Their treatment is easiest in
the second-quantised group field theory formalism which allows the adaptation
of techniques from the description of Bose-Einstein condensates in condensed
matter physics. Dynamical equations for the states can be derived directly from
the underlying quantum gravity dynamics. The analogue of the Gross-Pitaevskii
equation defines an anisotropic quantum cosmology model, in which the
condensate wavefunction becomes a quantum cosmology wavefunction on
minisuperspace. To illustrate this general formalism, we give a mapping of the
gauge-invariant geometric data for a tetrahedron to a minisuperspace of
homogeneous anisotropic 3-metrics. We then study an example for which we give
the resulting quantum cosmology model in the general anisotropic case and
derive the general analytical solution for isotropic universes. We discuss the
interpretation of these solutions. We suggest that the WKB approximation used
in previous studies, corresponding to semiclassical fundamental degrees of
freedom of quantum geometry, should be replaced by a notion of semiclassicality
that refers to large-scale observables instead.
