Chaos and a resonance mechanism for structure formation in inflationary models

摘要

We exhibit a resonance mechanism of amplification of density perturbations in inflationary models, using a minimal set of ingredients (an effective cosmological constant, a scalar field minimally coupled to the gravitational field and matter), common to most models in the literature of inflation. This mechanism is based on the structure of homoclinic cylinders, emanating from an unstable periodic orbit in the neighborhood of a saddle-center critical point, present in the phase space of the model. The cylindrical structure induces oscillatory motions of the scales of the universe whenever the orbit visits the neighborhood of the saddle-center, before the universe enters a period of exponential expansion. The oscillations of the scale functions produce, by a resonance mechanism, the amplification of a selected wave number spectrum of density perturbations, and can be used to explain the hierarchy of scales observed in the actual universe. The transversal crossings of the homoclinic cylinders induce chaos in the dynamics of the model - a fact closely connected to the resonance mechanism occurring immediately before the exit to inflation. [References: 10]