Semiclassical Limit of New Spin Foam Models

We study the problem of semiclassical limit of Loop Quantum Gravity theory defined by the new spin foam models. This is done by analyzing the large-spin asymptotics of the Hartle-Hawking wavefunction. By using the stationary phase method we determine the wavefunction asymptotics, which then determines the large-distance asymptotics of the corresponding graviton propagator. We show that the graviton propagator behaves as the inverse distance to the fourth power. Our result is a direct consequence of the large-spin asymptotics of the spin foam model vertex amplitude, and it is valid for all new spin foam models, since they all have the same type of the vertex amplitude asymptotics. We also find the type of the vertex amplitude asymptotics which gives the correct graviton propagator.