Spin foam propagator: A new perspective to include a cosmological constant

TL;DR

This paper examines the calculation of the graviton propagator in spin foam models with a cosmological constant, proposing alternative methods to avoid the problematic double scaling limit.

Contribution

It introduces new approaches to define the graviton propagator in spin foam models that include a cosmological constant, bypassing the double scaling limit.

Findings

Double scaling limit breaks down with cosmological constant

Proposes alternative definitions of the graviton propagator

Analyzes the model by Haggard, Han, Kaminski, and Riello

Abstract

In recent years, the calculation of the first non-vanishing order of the metric 2-point function or graviton propagator in a semiclassical limit has evolved as a standard test for the credibility of a proposed spin foam model. The existing results of spinfoam graviton propagator rely heavily on the so-called double scaling limit where spins $j$ are large and the Barbero-Immirzi parameter $\gamma$ is small such that the area $A\propto j\gamma$ is approximately constant. However, it seems that this double scaling limit is bound to break down in models including a cosmological constant. We explore this in detail for the recently proposed model by Haggard, Han, Kaminski and Riello and discuss alternative definitions of a graviton propagator, in which the double scaling limit can be avoided.