Asymptotic freedom from induced gravity cosmology

We give conditions to obtain cosmological asymptotic freedom in scalar-tensor theories of gravity. We show that this feature can be achieved in FRW flat spacetimes since we obtain singularity free solutions where the effective gravitational constant $G_{eff}\to 0$ for $t\to -\mathrm{\infty }$ and, for some of them, $G_{eff}\to G_N$ for $t\to \mathrm{\infty }$, where $G_N$ is the Newton constant.