Cosmological dynamics of scalar-tensor gravity

We study the phase space of Friedmann-Lemaitre-Robertson-Walker (FLRW) models derived from scalar-tensor gravity where the non-minimal coupling is F (phi) = xi phi(2) and the effective potential is V (phi) = lambda phi(n). Our analysis allows one to unfold many features of the cosmology of this class of theories. For example, the evolution mechanism towards states indistinguishable from GR is recovered and proved to depend critically on the form of the potential V (phi). Also, transient almost-Friedmann phases evolving towards accelerated expansion and unstable inflationary phases evolving towards stable ones are found. Some of our results are shown to hold also for the string-dilaton action.