Wormholes and naked singularities in Brans–Dicke cosmology

We perform an analytical and numerical study of static spherically symmetric solutions in the context of the Brans–Dicke-like cosmological model by Elizalde et al (2004 Phys. Rev. D 70 043539) with an exponential potential. In this model the phantom regime arises without the appearance of any ghost degree of freedom due to the specific form of coupling. For certain parameter ranges the model contains a regular solution that we interpret as a wormhole in an otherwise de Sitter Universe. We put several bounds on the parameter values: $\omega <0,{\alpha }^2/|\omega |<{10}^{-5},22.7\lesssim {\varphi }_0\lesssim 25$. The numerical solution could mimic the Schwarzschild one, so the original model is consistent with astrophysical and cosmological observational data. However, differences between our solution and the Schwarzschild one can be quite large, so black hole candidate observations could probably place further limits on the ${\varphi }_0$ value. (paper)