We study a general scalar-tensor theory with an arbitrary coupling function $\omega \left(\phi \right)$ but also an arbitrary dependence of the gravitational constant $G\left(\phi \right)$ in the cases in which either one of them, or both, do not admit an analytical inverse, as in the hyperextended inflationary scenario. We present the full set of field equations and study their cosmological behavior. We show that different scalar-tensor theories can be grouped in classes with the same solution for the scalar field.

• Received 27 March 1996

DOI:https://doi.org/10.1103/PhysRevD.54.7373