Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-06-04
Gen.Rel.Grav. 32 (2000) 105-125
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
TeX 19 pages, matches published version in G.R.G
Scientific paper
For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the `backreaction effect' of inhomogeneities on the average expansion of the model. A universal relation between `backreaction' and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to $a_D^{-2}$, the expansion law governing a generic domain can be found. However, as the general equations show, `backreaction' acts as to produce average curvature in the course of structure formation, even when starting with space sections that are spatially flat on average.
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