Minimal Coupling and Attractors

TL;DR

This paper investigates how minimal coupling of gravity to matter influences the evolution of cosmological models, revealing symmetries and attractors through analysis of the symplectic structure and Liouville measure.

Contribution

It demonstrates that rescaling freedom induces symmetries and explains the natural emergence of attractors in flat Robertson-Walker cosmologies.

Findings

Rescaling freedom leads to symmetry between trajectories.

Liouville measure explains the existence of attractors.

Attractors are naturally weighted by volume due to symplectic structure.

Abstract

The effects of minimally coupling a gravity to matter on a flat Robertson-Walker geometry are explored. Particular attention is paid to the evolution of the symplectic structure and the Liouville measure it defines. We show that the rescaling freedom introduced by choice of fiducial cell leads to a symmetry between dynamical trajectories, which together with the Liouville measure provides a natural volume weighting explanation for the generic existence of attractors.