A small cosmological constant from the modified Brans-Dicke theory - an interplay between different energy scales

In this paper we discuss a model in which the energy density, corresponding to the effective cosmological constant, after the $SU(2)\times U(1)$ symmetry breaking appears to be of the desired order of $10^{-48}\div 10^{-47} GeV^{4}$. The model contain two different energy scales, one of which is associated with the Higgs's vacuum expectation value. Another scale is of the order of $10^{21}GeV$ and defines the vacuum expectation value of the Brans-Dicke scalar field, non-minimally coupled to gravity, and sets the value of the Planck mass. Other (dimensionless) parameters are assumed not to contain hierarchical differences. The model is devoid of any fine-tuning and gives a small value of the effective cosmological constant even if the real "bare" cosmological constant is quite large.