This work concerns a generalization of property (RD) from discrete groups to twisted etale groupoids equipped with a length function. We show that, under the assumption that the etale groupoid is principal, twisted property (RD) is equivalent to polynomial growth. This generalizes a result of Chen and Wei concerning rapid decay for metric spaces with bounded geometry. Additionally, some permanence properties of groupoid (RD) are established.

This work was partially supported by NSF 1952693.