Criticality and Averaging in Cosmology
نویسنده
چکیده
We propose comparing cosmological solutions in terms of their total spatial volumes V (τ ) as functions of proper time τ , assuming synchronous gauge, and with this intention evaluate the variations of V (τ ) about the Friedmann-Lemâıtre-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 (τ ) 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 (τ ).
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