Wormhole solution free of ghosts in Einstein's gravity with two scalar fields

TL;DR

This paper presents a model of traversable wormholes in Einstein's gravity with two scalar fields that avoids ghost instabilities by imposing a specific constraint, resulting in a stable wormhole solution.

Contribution

It introduces a novel constraint to eliminate ghosts in wormhole models with scalar fields, ensuring stability despite broken energy conditions.

Findings

Ghosts can be eliminated by a mimetic constraint.

The model admits stable, traversable wormholes.

No unstable modes are found in the solution.

Abstract

In this paper, we construct models that admit the traversable wormhole geometries in the framework of Einstein's gravity with two scalar fields. As well known, the energy conditions are broken and we show that there appears a ghost. The ghost can be, however, eliminated by imposing a constraint on the ghost field, which is a scalar. The constraint is similar to the mimetic one proposed by Chamseddine and Mukhanov to construct an alternative description of cold dark matter. We explicitly show that there does not appear any unstable mode although the energy conditions are broken. Therefore we obtain a model that realizes the traversable and stable wormhole.