Maximally symmetric spaces in Brans-Dicke theory and the cosmological constant

In this note we discuss a toy model in which the value of the effective cosmological constant is associated with a symmetry properties of the vacuum background solution and defined by the model parameter associated with a scalar field non-minimally coupled to gravity. Although the parameters in the model seem to have unrealistic values to account for the present value of the cosmological constant, the model demonstrates a possible alternative way it can arise.