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.