Wormholes and Naked Singularities in Brans-Dicke cosmology

We perform analytical and numerical study of static spherically symmetric solutions in the context of Brans-Dicke-like cosmological model by Elizalde et al. 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 the certain parameter ranges the model contains a regular solution which we interpret as a wormhole in an otherwise dS Universe. We put several bounds on the parameter values: $\omega<0 ,\,\, \alpha^2/|\omega|<10^{-5},22.7\lesssim\!\phi_0\!\lesssim25\,$. 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 $\phi_0$ value.