Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-07-29
Prog.Theor.Phys. 102 (1999) 1001-1013
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, PTPTeX, some minor corrections, final version for publication in Prog. Theor. Phys
Scientific paper
10.1143/PTP.102.1001
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 $V(\tau)$.
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