Behavior of cosmological models with varying $G$

We provide a detailed analysis of Friedmann-Robertson-Walker universes in a wide range of scalar-tensor theories of gravity. We apply solution-generating methods to three parametrized classes of scalar-tensor theory which lead naturally to general relativity in the weak-field limit. We restrict the parameters which specify these theories by the requirements imposed by the weak-field tests of gravitation theories in the solar system and by the requirement that viable cosmological solutions be obtained. We construct a range of exact solutions for open, closed, and flat isotropic universes containing matter with equation of state $p<~$$\frac{1}{3}$$\rho$ and in vacuum. We study the range of early- and late-time behaviors displayed, examine when there is a “bounce” at early times, and expansion maxima in closed models.