No realistic wormholes from ghost-free scalar-tensor phantom dark energy

TL;DR

This paper proves that viable scalar-tensor dark energy models with phantom behavior cannot form wormholes unless the coupling function becomes negative or zero, which leads to instability or fine-tuning issues.

Contribution

It demonstrates the impossibility of wormhole formation in standard scalar-tensor dark energy models with positive coupling functions, clarifying conditions for potential solutions.

Findings

Wormholes cannot form if the coupling function is positive everywhere.

Allowing the coupling function to reach zero or become negative can lead to solutions, but with stability issues.

Solutions with negative coupling function are generally unstable under perturbations.

Abstract

It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(\Phi)$ is everywhere positive and the scalar field $\Phi$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(\Phi)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions require severe fine tuning and a very peculiar kind of model. If $f < 0$ is allowed, it is argued (and confirmed by previous investigations) that such solutions are generically unstable under non-static perturbations, the instability appearing right near transition surfaces to negative $f$.