Abstract
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(\(\tilde R\)) 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(\(\tilde R\)) 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(\(\tilde R\)) that has a wormhole solution. For small values of the Ricci scalar, this f(\(\tilde R\)) agrees with the wormhole solution obtained for the higher-order gravity theory \(\tilde R + \varepsilon \tilde R^2 ,\varepsilon < 0\).
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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 173, No. 3, pp. 468–478, December, 2012.
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Darabi, F. Classical Euclidean wormhole solutions in the Palatini f(\(\tilde R\)) cosmology. Theor Math Phys 173, 1734–1742 (2012). https://doi.org/10.1007/s11232-012-0144-0
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DOI: https://doi.org/10.1007/s11232-012-0144-0