Deformation of the EPRL spin foam model by a cosmological constant

TL;DR

This paper extends a deformation of the EPRL spin foam model by a cosmological constant to arbitrary vertices, analyzing its large-spin asymptotics and showing it reproduces the Regge action with a cosmological term.

Contribution

It generalizes Han's deformation to arbitrary vertices and computes the large-j asymptotics, linking the Hessian determinant to the undeformed case.

Findings

Asymptotic formula recovers Regge action plus cosmological constant.

Hessian determinant relates to the undeformed vertex.

Deformation consistent with known 4-simplex case.

Abstract

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.