$w=-1$ as an Attractor

TL;DR

This paper investigates the role of the condition $w=-1$ as an attractor in cosmological models, showing that maximally expanding solutions with $P=- ho$ are generically attractors in both homogeneous and anisotropic settings.

Contribution

It extends the concept of attractors in flat Robertson-Walker geometries to inhomogeneous and anisotropic cosmological models, highlighting the significance of $w=-1$ solutions.

Findings

Maximally expanding solutions are attractors in the phase space.

Phase-space measures sharply peak around solutions with $P=- ho$.

Attractors persist in inhomogeneous and anisotropic contexts.

Abstract

It has recently been shown, in flat Robertson-Walker geometries, that the dynamics of gravitational actions which are minimally coupled to matter fields leads to the appearance of "attractors" - sets of physical observables on which phase space measures become peaked. These attractors will be examined in the context of inhomogeneous perturbations about the FRW background and in the context of anisotropic Bianchi I systems. We show that maximally expanding solutions are generically attractors, i.e. any measure based on phase-space observables becomes sharply peaked about those solutions which have $P=-\rho$.