Chaos and universality in the dynamics of inflationary cosmologies. II. The role of nonextensive statistics

Nonlinear Sciences – Chaotic Dynamics

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Particle-Theory And Field-Theory Models Of The Early Universe, Numerical Relativity

Scientific paper

We discuss universal statistical patterns in the chaotic dynamics of closed inflationary cosmologies, associated with the presence of a saddle-center critical point in the phase space of the models. We extend and complete the analysis made in a previous paper [H. P. de Oliveira, S. L. Sautu, I. Damião Soares, and E. V. Tonini, Phys. Rev. D 60, 121301 (1999)], including also other inflationary models. The statistical distribution connected to orbits that visit a neighborhood of the saddle center is shown to be in the realm of Tsallis nonextensive statistics that generalizes the Boltzmann-Gibbs statistics for systems in which long-range interactions are present. The value of the entropic index q of the distribution function determines the dimension of the fractal basin boundaries in the ensemble of initial conditions, with respect to the code recollapse/escape into inflation. In a regime of high nonintegrability, this distribution is universal in the sense that it is scale invariant, independent of the parameters of the model and independent of the particular system where the saddle-center is present. Also it does not depend on the specific model where the saddle-center is present. The consequences for the physics of the early stages of inflation are discussed.

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