Coupling constant constraints in a nonminimally coupled phantom cosmology

In the paper we investigate observational constraints on coupling to gravity constant parameter $\xi$ using distant supernovae SNIa data, baryon oscillation peak (BOP), the cosmic microwave background radiation (CMBR) shift parameter, and $H(z)$ data set. We estimate the value of this parameter to constrain the extended quintessence models with nonminimally coupled to gravity phantom scalar field. The combined analysis of observational data favors a value of $\xi$ which lies in close neighborhood of the conformal coupling. While our estimations are model dependent they give rise to a indirect bound on the Equivalence Principle.