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We study the classical Euclidean wormholes in the context of extendedtheories of gravity. With no loss of generality, we use the dynamicalequivalence between $f(\tilde{R})$ gravity and scalar-tensor theories toconstruct a point-like Lagrangian in the flat FRW space time. We first show thedynamical equivalence between Palatini $f(\tilde{R})$ gravity and theBrans-Dicke theory with self-interacting potential, and then show the dynamicalequivalence between the Brans-Dicke theory with self-interacting potential andthe minimally coupled O'Hanlon theory. We show the existence of new Euclideanwormhole solutions for this O'Hanlon theory and, for an special case, find outthe corresponding form of $f(\tilde{R})$ having wormhole solution. For smallvalues of the Ricci scalar, this $f(\tilde{R})$ is in agreement with thewormhole solution obtained for higher order gravity theory $\tilde{R}+\epsilon\tilde{R}^2,\epsilon<0$.

Classical Euclidean wormhole solutions in Palatini $f(\tilde{R})$ cosmology