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

It is proven that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ( w < −1) behavior in cosmology, even in the presence of electric or magnetic fields, if the nonminimal coupling function f (Φ) is positive everywhere and the scalar field Φ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if f (Φ) 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 nonstatic perturbations, the instability appearing right near transition surfaces to negative f .