  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.
