What can we learn from nonminimally coupled scalar field cosmology?

A novel exploration of nonminimally coupled scalar field cosmology is propo sed in the framework of spatially flat Friedmann-Robertson-Walker spaces fo r arbitrary scaler field potentials V(psi) and values of the nonminimal cou pling constant xi. This approach is self-consistent in the sense that the e quation of state of the scalar field is not prescribed a priori, but is rat her 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 invo lved 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 organizat ion of the phase space of the dynamical system. New exact solutions sharing a universal character are presented; one of them describes a nonsingular u niverse that exhibits a graceful exit from, and entry into, inflation. This behavior does not require the presence of the cosmological constant. The r elevance of this solution and of the topological structure of the phase spa ce with respect to an emergence of the universe from a primordial Minkowski vacuum, in an extended semiclassical context, is shown.