Scalar-tensor cosmologies: fixed points of the Jordan frame scalar field

We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe the details of the phase space geometry. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and matter domination. There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System PPN constraints. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points (attractor or other). PACS: 98.80.Jk, 04.50.+h, 04.40.Nr 1 Electronic address: [email protected] 2 Electronic address: [email protected] 3 Electronic address: [email protected]