Graviton propagator asymptotics and the classical limit of ELPR/FK spin\n foam models

We study the classical limit of the ELPR/FK spin foam models by analyzing the\nlarge-distance asymptotics of the corresponding graviton propagators. This is\ndone by examining the large-spin asymptotics of the Hartle-Hawking wavefunction\nwhich is peaked around a classical flat spatial geometry. By using the\nstationary phase method we determine the wavefunction asymptotics. The obtained\nasymptotics does not give the desired large-distance asymptotics for the\ncorresponding graviton propagator. However, we show that the ELPR/FK vertex\namplitude can be redefined such that the corresponding Hartle-Hawking\nwavefunction gives the desired asymptotics for the graviton propagator.\n