Criticality and Averaging in Cosmology

TL;DR

This paper investigates the stability of FLRW cosmological solutions by analyzing variations in spatial volume over time, showing they are critical points and supporting their interpretation as averaged models.

Contribution

It introduces a method to evaluate variations of spatial volume in cosmological solutions without solving perturbation equations, demonstrating FLRW solutions are critical points in this context.

Findings

FLRW solutions are critical points for spatial volume variations.

First variations vanish in non-homogeneous and non-isotropic directions.

Supports the interpretation of FLRW solutions as averaged cosmological models.

Abstract

We propose comparing cosmological solutions in terms of their total spatial volumes $V(\tau)$ as functions of proper time $\tau$, assuming synchronous gauge, and with this intention evaluate the variations of $V(\tau)$ about the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions for dust. This can be done successfully in a simple manner without solving perturbation equations. In particular, we find that first variations vanish with respect to all directions which do not possess homogeneity and isotropy preserving components; in other words, every FLRW solution is a {\it critical point} for $V(\tau)$ in the properly restricted subspace of the space of solutions. This property may support a validity of the interpretation of the FLRW solutions as constituting an averaged model. We also briefly investigate the second variations of $V(\tau)$.