The dynamical system approach to scalar field cosmology

A spatially flat FLRW universe (motivated by inflation) is studied; by a di mensional reduction of the dynamical equations of scalar field cosmology, i t is demonstrated that a spatially flat universe cannot exhibit chaotic beh aviour. The result holds when the source of gravity is a non-minimally coup led scalar field, for any self-interaction potential and for arbitrary valu es of the coupling constant with the Ricci curvature. The phase space of th e dynamical system is studied, and regions inaccessible to the evolution ar e found. The topology of the forbidden regions, their dependence on the parameters, the fixed points and their stability character, and the asymptotic behaviou r of the solutions are studied. New attractors are found, in addition to th ose known from the minimal coupling case, certain exact solutions are prese nted and the implications for inflation are discussed. The equation of stat e is not prescribed a priori, but rather is deduced self-consistently from the field equations.