Criticality and Averaging in Cosmology

We propose comparing cosmological solutions in terms of their total spatialvolumes $V(\tau)$ as functions of proper time $\tau$, assuming synchronousgauge, and with this intention evaluate the variations of $V(\tau)$ about theFriedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) solutions for dust. This can bedone successfully in a simple manner without solving perturbation equations. Inparticular, we find that first variations vanish with respect to all directionswhich do not possess homogeneity and isotropy preserving components; in otherwords, every FLRW solution is a {\it critical point} for $V(\tau)$ in theproperly restricted subspace of the space of solutions. This property maysupport a validity of the interpretation of the FLRW solutions as constitutingan averaged model. We also briefly investigate the second variations of$V(\tau)$.Comment: 12 pages, PTPTeX, some minor corrections, final version for publication in Prog. Theor. Phy