Chaos and universality in the dynamics of inflationary cosmologies

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 models. The hyperbolic energy of orbits visiting a neighborhood of the saddle-center has a random distribution with respect to the ensemble of initial conditions, but the associated histograms define a statistical distribution law of the form ${p\left(x\right)=Cx}^{-\gamma },$ for almost the whole range of hyperbolic energies considered. We present numerical evidence that $\gamma$ determines the dimension of the fractal basin boundaries in the ensemble of initial conditions. This distribution is universal in the sense that it does not depend on the parameters of the models and is scale invariant. We discuss possible physical consequences of this universality for the physics of inflation.