As was emphasized in the preceding chapter, the way the scalar field enters the arena of the scalar–tensor theory is not simple. It does so through what is known as a nonminimal coupling term. This is a unique feature shared by those models qualified to be called scalar–tensor theories in the sense conceived by Jordan. In spite of the simplicity of wanting to implement a variable gravitational “constant,” this term is a somewhat contrived technical device that tends to obscure other issues of physical significance. One of the emphases in this chapter is placed on revealing them beyond mathematical manipulations.
Among several versions, or models, of the scalar–tensor theory, the one due to Brans and Dicke might be viewed as a “prototype.” This model, which is based on certain assumptions made for the sake of simplicity, is in fact over-simplified from the point of view of theoretical models of the modern unification program. Also for some other reasons, this model may not be accepted as fully realistic. Nevertheless, a prototype has its own merit that deserves careful and comprehensive understanding. In this chapter we introduce the original BD model as a basis of the subsequent developments.
Section 1 is an elementary but technical introduction to the prototype BD model as a basis of the whole discussion that follows.