  In this article, we consider an ad-hoc deformation of the EPRL model for
quantum gravity by a cosmological constant term. This sort of deformation has
been first introduced by Han for the case of the $4$-simplex. In this article,
we generalise the deformation to the case of arbitrary vertices, and compute
its large-$j$-asymptotics. We show that, if the boundary data corresponds to a
$4d$ polyhedron $P$, then the asymptotic formula gives the usual Regge action
plus a cosmological constant term. We pay particular attention to the
determinant of the Hessian matrix, and show that it can be related to the one
of the undeformed vertex.
