Chaos and Universality in the Dynamics of Inflationary Cosmologies

TL;DR

This paper uncovers a universal statistical pattern in the chaotic dynamics of inflationary cosmologies, revealing scale-invariant distributions and fractal boundary dimensions that may influence inflation physics.

Contribution

It introduces a new universal distribution law for hyperbolic energies in inflationary models and links it to fractal basin boundary dimensions.

Findings

Hyperbolic energy distribution follows a power law $p(x) = C x^{-eta}$.

The exponent $eta$ determines the fractal dimension of basin boundaries.

The distribution law is universal and scale-invariant across models.

Abstract

We describe a new statistical pattern in the chaotic dynamics of closed inflationary cosmologies, associated with the partition of the Hamiltonian 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 $p(x) = C x^{-\gamma}$, 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.tribution law of the form $p(x) = C x^{-\gamma}$, 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.