Chaos and Universality in the Dynamics of Inflationary Cosmologies.pdf

Chaos and Universality in the Dynamics of Inflationary Cosmologies H. P. de Oliveira∗ , S. L. Sautu† Universidade do Estado do Rio de Janeiro Instituto de F´ısica - Departamento de F´ısica Te´orica, CEP 20550-013 Rio de Janeiro, RJ, Brazil. I. Dami˜ao Soares‡ and E. V. Tonini§ Centro Brasileiro de Pesquisas F´ısicas Rua Dr. Xavier Sigaud, 150 CEP 22290-180, Rio de Janeiro, RJ, Brazil. We describe a new statistical pattern in the chaotic dynamics of closed inflationary cosmologies, associated with the partition of the Hamiltonian into rotational motion energy and hyperbolic motion energy pieces, in a linear neighborhood of the saddle-center present in the phase space of the 9 models. The hyperbolic energy of orbits visiting a neighborhood of the saddle-center has a random 9 distribution with respect to the ensemble of initial conditions, but the associated histograms define 9 −γ 1 a statistical distribution law of the form p (x) = C x , for almost the whole range of hyperbolic energies considered. We present numerical evidence that γ determines the dimension of the fractal p basin boundaries in the ensemble of initial conditions. This distribution is universal in the sense e