  This paper investigates the critical behaviors of the 4-dimensional spinfoam
model with cosmological constant for a general 4-dimensional simplicial complex
as the discretization of spacetime. We find that, at the semi-classical regime,
the spinfoam amplitude is peaked at the real critical points that correspond to
zero deficit angles (modulo $4\pi\mathbb{Z}/\gamma$) hinged by internal
triangles of the 4-complex. Since the 4-simplices from the model are of
constant curvature, the discrete geometry with zero deficit angle manifests a
de Sitter (dS) spacetime or an anti de Sitter (AdS) spacetime depending on the
sign of the cosmological constant fixed by the boundary condition. The
non-(A)dS spacetimes emerge from the complex critical points by an analytic
continuation to complex configurations.
