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

TL;DR

This paper explores Euclidean wormhole solutions within Palatini $f( ilde{R})$ gravity, establishing equivalences with scalar-tensor theories and identifying specific $f( ilde{R})$ forms that admit wormhole solutions, including a case matching quadratic gravity.

Contribution

It demonstrates the existence of Euclidean wormholes in Palatini $f( ilde{R})$ gravity by establishing equivalences with scalar-tensor theories and deriving explicit $f( ilde{R})$ forms supporting wormholes.

Findings

Existence of Euclidean wormholes in Palatini $f( ilde{R})$ gravity.

Derived specific $f( ilde{R})$ functions supporting wormhole solutions.

Found correspondence with quadratic gravity for small Ricci scalar.

Abstract

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