  The present acceleration of the Universe strongly indicated by recent
observational data can be modeled in the scope of a scalar-tensor theory of
gravity. We show that it is possible to determine the structure of this theory
(the scalar field potential and the functional form of the scalar-gravity
coupling) along with the present density of dustlike matter from the following
two observable cosmological functions: the luminosity distance and the linear
density perturbation in the dustlike matter component as functions of redshift.
Explicit results are presented in the first order in the small inverse
Brans-Dicke parameter 1/omega.
