Geodesic
Classical Euclidean wormhole solutions in the~Palatini $f(\widetilde R)$ cosmology
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 468-478

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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 $\widetilde R+\epsilon \widetilde R^2$, $\epsilon0$.
Keywords: Euclidean wormhole, $f(R)$ cosmology, scalar–tensor theory. 
@article{TMF_2012_173_3_a7,
     author = {F. Darabi},
     title = {Classical {Euclidean} wormhole solutions in {the~Palatini} $f(\widetilde R)$ cosmology},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {468--478},
     publisher = {mathdoc},
     volume = {173},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a7/}
}
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F. Darabi. Classical Euclidean wormhole solutions in the~Palatini $f(\widetilde R)$ cosmology. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 468-478. http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a7/