Classical Euclidean wormhole solutions in the Palatini $f(\widetilde R)$ cosmology

We study the classical Euclidean wormholes in the context of extended theories of gravity. Without loss of generality, we use the dynamical equivalence between $f(\widetilde R)$ gravity and scalar–tensor theories to construct a pointlike Lagrangian in the flat Friedmann–Robertson–Walker space–time. We first show the dynamical equivalence between the Palatini $f(\widetilde R)$ gravity and the Brans–Dicke theory with a self-interaction potential and then show the dynamical equivalence between the Brans–Dicke theory with a self-interaction potential and the minimally coupled O'Hanlon theory. We show the existence of new Euclidean wormhole solutions for this O'Hanlon theory; in a special case, we find the corresponding form of $f(\widetilde R)$ that has a wormhole solution. For small values of the Ricci scalar, this $f(\widetilde R)$ agrees with the wormhole solution obtained for the higher-order gravity theory $\widetilde R+\epsilon \widetilde R^2$, $\epsilon<0$.