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

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(Φ) is everywhere positive 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 non-static perturbations, the instability appearing right near transition surfaces to negative f . PACS numbers: 04.50.+h, 04.70.-s, 95.36.+x 1. Wormholes are hypothetic objects described by nonsingular solutions of gravitational field equations with two large or infinite regions of space-time connected by a throat (a tunnel). These two regions may lie in the same universe or even in different universes. The existence of stable static or stationary (traversable, Lorentzian) wormholes can lead to remarkable astrophysical effects as was recently emphasized in [1], as well as to the possibility of realizing hyperspace jumps (‘nulltransportation’) or time machines [2]. That is why it is so important to investigate if really existing matter can produce and support such objects (it is well known that vacuum Einstein equations do not admit static wormhole solutions). It is not difficult to construct a static wormhole without worrying about a matter source, as was done, e.g., by Morris and Thorne [3]. Problems arise when trying to find an explicit, internally self-consistent matter model whose energy-momentum tensor (EMT) has a structure required for wormhole existence and stability. Really, it is known that such matter should be rather exotic in the sense that its effective EMT should violate the weak or/and null energy conditions