Emergence of a low spin phase in group field theory condensates
  Recent results have shown how quantum cosmology models can be derived from
the effective dynamics of condensate states in group field theory (GFT), where
'cosmology is the hydrodynamics of quantum gravity': the classical Friedmann
dynamics for homogeneous, isotropic universes, as well as loop quantum
cosmology (LQC) corrections to general relativity have been shown to emerge
from fundamental quantum gravity. We take one further step towards
strengthening the link with LQC and show, in a class of GFT models for gravity
coupled to a free massless scalar field and for generic initial conditions,
that GFT condensates dynamically reach a low spin phase of many quanta of
geometry, in which all but an exponentially small number of quanta are
characterised by a single spin $j_0$ (i.e. by a constant volume per quantum).
As the low spin regime is reached, GFT condensates expand to exponentially
large volumes, and the dynamics of the total volume follows precisely the
classical Friedmann equations. This behaviour follows from a single requirement
on the couplings in the GFT model under study. We present one particular simple
case in which the dominant spin is the lowest one: $j_0=0$ or, if this is
excluded, $j_0=1/2$. The type of quantum state usually assumed in the
derivation of LQC is hence derived from the quantum dynamics of GFT. These
results confirm and extend recent results by Oriti, Sindoni and Wilson-Ewing in
the same setting.
