Evolution of homogeneous and isotropic scalar-tensor cosmological models

Homogeneous and isotropic cosmological models are considered in the framework of general scalar-tensor theories of gravity with arbitrary coupling function and scalar potential. Nonlinear approximate equations are derived for the regime close to the so-called limit of general relativity where the local observational constraints are satisfied. Approximate solutions in cosmological time are presented for the potential dominated era and for the era when the energy density of ordinary matter dominates over the energy density of scalar potential.