Brans-Dicke cosmology does not have the ΛCDM phase as a universal attractor

In this paper we seek for relevant information on the asymptotic cosmological dynamics of the Brans-Dicke theory of gravity for several self-interaction potentials. By means of the simplest tools of the dynamical systems theory, it is shown that the general relativity de Sitter solution is an attractor of the Jordan frame (dilatonic) Brans-Dicke theory only for the exponential potential U(phi) proportional to exp phi, which corresponds to the quadratic potential V(phi) proportional to phi(2) in terms of the original Brans-Dicke field. phi = exp phi, or for potentials which approach to exp f at the stable point. At the de Sitter attractor, as well as at the stiff-matter equilibrium configurations, the dilaton is necessarily massless. We find bounds on the Brans-Dicke coupling constant omega(BD), which are consistent with well-known results.