  We apply the technique of spinfoam to study the space-time which,
classically, contains a curvature singularity. We derive from the full
covariant Loop Quantum Gravity (LQG) that the region near curvature singularity
has to be of strong quantum gravity effect. We show that the spinfoam
configuration describing the near-singularity region has to be of small spins
$j$, in order that its contribution to the full spinfoam amplitude is
nontrivial. The spinfoams in low and high curvature regions of the space-time
may be viewed as in two different {phases} of covariant LQG. There should be a
phase transition as the space-time described by spinfoam becomes more and more
curved. A candidate of order parameter is proposed for understanding the phase
transition. Moreover, we also analyze the spin-spin correlation function of
spinfoam, and show the correlation is of long-range in the low curvature phase.
This work is a first step toward understanding the physics of black hole and
early universe from the full covariant LQG theory.
