  We consider the anomaly induced effective action in N=4 super Yang-Mills
theory in interaction with the Brans-Dicke (BD) field. The generalization of
the BD theory so as to permit an energy exchange between the scalar field and
ordinary matter fields, was recently worked out by T. Clifton and J. D. Barrow
[Phys. Rev. D 73, 104022 (2006)]. We derive the scalar field equations for the
dilaton field, and the BD field, and discuss the Friedmann equation in the
general case. The present paper is a continuation of an investigation some
years ago dealing with the case of conformal anomaly plus ordinary classical
gravity [I. Brevik and S. D. Odintsov, Phys. Lett. B 455, 104 (1999)].
