1998/07/15 by H. P. de Oliveira, H. P. DE OLIVEIRA, I. Damião Soares +2
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #Earth Systems and Cosmic Evolution #Scientific Research and Discoveries #gr-qc
paper · pdf · doi:10.1142/s0217732398001972
published as Mod.Phys.Lett. A13 (1998) 1881-1886 · 4 pages. This essay received an Honorable Mention from the Gravity Research Foundation, 1998-Ed. To appear in Mod. Phys. Lett. A
arxiv created 1998/07/15 · openalex publication_date 1998/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.