Towards Spinfoam Cosmology
  We compute the transition amplitude between coherent quantum-states of
geometry peaked on homogeneous isotropic metrics. We use the holomorphic
representations of loop quantum gravity and the
Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at
first order in the vertex expansion, second order in the graph (multipole)
expansion, and first order in 1/volume. We show that the resulting amplitude is
in the kernel of a differential operator whose classical limit is the canonical
hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an
indication that the dynamics of loop quantum gravity defined by the new vertex
yields the Friedmann equation in the appropriate limit.
