What can we learn from nonminimally coupled scalar field cosmology?

A novel exploration of nonminimally coupled scalar field cosmology is proposed in the framework of spatially flat Friedmann-Robertson-Walker spaces for arbitrary scaler field potentials V(psi) and values of the nonminimal coupling constant xi. This approach is self-consistent in the sense that the equation of state of the scalar field is not prescribed a priori, but is rather deduced together with the solution of the field equations. The role of nonminimal coupling appears to be essential. A dimensional reduction of the system of differential equations leads to the result that chaos is absent in the dynamics of a spatially flat FRW universe with a single scaler field. The topology of the phase space is studied and reveals an unexpected involved structure: according to the form of the potential V(psi) and the value of the nonminimal coupling constant xi, dynamically forbidden regions may exist. Their boundaries play an important role in the topological organization of the phase space of the dynamical system. New exact solutions sharing a universal character are presented; one of them describes a nonsingular universe that exhibits a graceful exit from, and entry into, inflation. This behavior does not require the presence of the cosmological constant. The relevance of this solution and of the topological structure of the phase space with respect to an emergence of the universe from a primordial Minkowski vacuum, in an extended semiclassical context, is shown.