Chaotic Friedmann-Robertson-Walker Cosmology

TL;DR

This paper demonstrates that a closed Friedmann-Robertson-Walker universe with a massive scalar field exhibits chaos, limiting predictability of the universe's evolution near the Big Crunch due to the breakdown of integrability.

Contribution

It provides a novel analysis showing how chaos arises in this cosmological model through the breakdown of adiabatic integrability and numerical Lyapunov exponent evaluation.

Findings

Chaos occurs for large scalar field amplitudes.

Adiabatic approximation shows integrability; non-adiabatic terms cause chaos.

Lyapunov exponents confirm chaotic dynamics.

Abstract

We show that the dynamics of a spatially closed Friedmann - Robertson - Walker Universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is integrable under the adiabatic approximation, but that the corresponding KAM tori break up when non adiabatic terms are considered. This finding is confirmed by numerical evaluation of the Lyapunov exponents associated with the system, among other criteria. Chaos sets strong limitations to our ability to predict the value of the field at the Big Crunch, from its given value at the Big Bang. (Figures available on request)