Chaos and a Resonance Mechanism for Structure Formation in Inflationary Models

TL;DR

This paper presents a resonance mechanism involving homoclinic cylinders that amplifies density perturbations during inflation, potentially explaining the universe's scale hierarchy through chaotic dynamics near a saddle-center point.

Contribution

It introduces a novel resonance mechanism based on homoclinic cylinders in inflationary models, linking chaos to structure formation in the early universe.

Findings

Resonance amplifies specific density perturbation modes.

Homoclinic cylinders induce oscillatory behavior in the universe's scale.

Chaos arises from crossings of homoclinic cylinders, affecting inflation dynamics.

Abstract

We exhibit a resonance mechanism of amplification of density perturbations in inflationary mo-dels, 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 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 intimately connected to the resonance mechanism occuring immediately before the exit to inflation.