288 Gravitational instability in Newtonian theory
are formed. The walls connect the filaments. It is clear that in those places where
α, β, γare all negative (valleys) the expansion will continue forever. Matter will
be diluted in these regions and empty voids, occupying most of the volume, will be
produced.
Over time these anisotropic structures simply become elements of the structure
forming on even larger scales. Finally the anisotropic substructure of the larger
structural units becomes virialized and disappears. That is, the web of filaments
and walls is only an intermediate stage of evolution between an initial, nearly
homogeneous state and a final, virialized isotropic structure.
At present we observe filaments and pancakes on scales which entered the non-
linear stage not very long ago. Therefore their average density is only a few times
greater than the average density in the universe. The filaments connect quasi-
spherical structures, in which the density is larger than in filaments.
Baryons fall into the potential wells created by the cold dark matter and form
luminous galaxies. Most of the galaxies are concentrated in the quasi-spherical
inhomogeneities corresponding to clusters and superclusters of galaxies with scales
of order of a few Mpc.Some of them reside in filaments which have scales of 10–30
Mpc, and others are yet in pancakes.
The complete quantitative theory of the structure formation is a challenging
numerical problem and represents a frontier of current research.