Criticality and Averaging in Cosmology

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\^ıtre-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 $V(\tau )$.

12 pages, PTPTeX, some minor corrections, final version for publication in Prog. Theor. Phys

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