Spinfoam cosmology with the proper vertex amplitude
  The proper vertex amplitude is derived from the EPRL vertex by restricting to
a single gravitational sector in order to achieve the correct semi-classical
behaviour. We apply the proper vertex to calculate a cosmological transition
amplitude that can be viewed as the Hartle-Hawking wavefunction. To perform
this calculation we deduce the integral form of the proper vertex and use
extended stationary phase methods to estimate the large-volume limit. We show
that the resulting amplitude satisfies an operator constraint whose classical
analogue is the Hamiltonian constraint of the Friedmann-Robertson-Walker
cosmology. We find that the constraint dynamically selects the relevant family
of coherent states and demonstrate a similar dynamic selection in standard
quantum mechanics. We investigate the effects of dynamical selection on
long-range correlations.
