Exact solutions of the Hyperextended Scalar Tensor theory with potential in the Bianchi type I model

The Hyperextended Scalar Tensor theory with a potential is defined by three free functions: the gravitational function, the Brans-Dicke coupling function and the potential. Starting from the expression of the 3-volume and the potential as function of the proper time, we determine the exact solutions of this theory. We study two important cases corresponding to power and exponential laws for the 3-volume and the potential.