  Higher derivative terms in the gravitational action are natural from the
perspective of quantum gravity, but are perceived as leading to a lack of
well-posedness. The Gauss Bonnet term has second-order equations of motion, but
does not impact gravitational dynamics in 4D, so one might expect that it is
not physically relevant. We discuss how signatures can show up in tunnelling
processes and whether these will likely be physically accessible in Higgs
vacuum decay.
