No-chaos theorem for non-minimally coupled scalar field cosmology and a new cosmogenesis scenario

A general dynamical system approach to classical sell-consistent scaler field cosmology is presented in the framework of spatially flat FLRW space-times, for arbitrary potentials and arbitrary non-minimal coupling. We show that these universes cannot undergo chaotic behaviors, thus suggesting a possible new role of inflation in cosmology. An unexpectedly involved topology of the phase-portrait of the cosmological dynamics is exhibited: Dynamically forbidden regions, playing a crucial dynamical role, appear. A new exact critical solution, a heteroclinic orbit, connects two de Sitter inflationary regimes. We suggest a novel intriguing semiclassical cosmogenesis scenario in which the quantized scalar field could tunnel through the classically forbidden region, from the Minkowski space-time towards the nearest classically allowed solution: The critical one.