Averaging inhomogeneous Newtonian cosmologies.
Abstract
Idealizing matter as a pressureless fluid and representing its motion by a peculiarvelocity field superimposed on a homogeneous and isotropic Hubble expansion, we apply (Lagrangian) spatial averaging on an arbitrary domain D to the (nonlinear) equations of Newtonian cosmology and derive an exact, general equation for the evolution of the (domain dependent) scale factor a_D_(t). We consider the effect of inhomogeneities on the average expansion and discuss under which circumstances the standard description of the average motion in terms of Friedmann's equation holds. We find that this effect vanishes for spatially compact models if one averages over the whole space. For spatially infinite inhomogeneous models obeying the cosmological principle of largescale isotropy and homogeneity, Friedmann models may provide an approximation to the average motion on the largest scales, whereas for hierarchical (Charliertype) models the general expansion equation shows how inhomogeneities might appreciably affect the expansion at all scales. An averaged vorticity evolution law is also given. Since we employ spatial averaging, the problem of justifying ensemble averaging does not arise. A generalization of the expansion law to general relativity is straightforward for the case of irrotational flows and will be discussed. The effect may have important consequences for a variety of problems in largescale structure modeling as well as for the interpretation of observations.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 1997
 arXiv:
 arXiv:astroph/9510056
 Bibcode:
 1997A&A...320....1B
 Keywords:

 GRAVITATION;
 INSTABILITIES;
 METHODS: ANALYTICAL;
 COSMOLOGY: THEORY;
 LARGESCALE STRUCTURE OF UNIVERSE;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 Astron. Astrophys., in press (substantial extensions