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No realistic wormholes from ghost-free scalar-tensor phantom dark energy
K. A. Bronnikov, A. A. Starobinsky+
Centre of Gravitation and Fundamental Metrology, VNIIMS, 117361 Moscow, Russia;
Institute of Gravitation and Cosmology, PFUR, 117198 Moscow, Russia
+Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

PACS: 04.50.+h, 04.70.-s, 95.36.+x
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.

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