Criticality and Averaging in Cosmology

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&icirctre-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 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).