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Gravitational Instability

  According to the standard world picture, often referred to as the ``standard model'' (``Big Bang'' is somewhat misguiding), the Universe is approximately homogeneous on average over large enough scales. ``Large enough'' can be justified to be scales of size about 100 tex2html_wrap_inline5209 Mpc (comparably, the size of the observable Universe is about 3000 tex2html_wrap_inline5209 Mpc, in metric distance). The homogeneity requirement can also be applied very early in the history of the Universe, assuming an expanding Friedmann-Lemaître model. According to the gravitational instability theory, perturbations must have grown from small departures in this seemingly homogeneous mass distribution to the large-scales structures we observe today; such as galaxies, groups of galaxies, clusters, and even superclusters ( tex2html_wrap_inline5243 Mpc). These density fluctuations where present at the decoupling of matter and radiation at redshift tex2html_wrap_inline5245 . Let us first take a look at how they grew from there.

The description of the gravitational instability theory can be found in numerous texts, e.g. Pad and P-80,P-93. I will follow the description of the latter two except where noted.

Perturbations of the density, or the density contrast, is given by tex2html_wrap_inline5247 . The mass density is then


where tex2html_wrap_inline5249 is the mean background mass density. Note that the spatial coordinates tex2html_wrap_inline5251 are comoving; i.e. expanding with the model. One can imagine that tex2html_wrap_inline5251 is the coordinates of a freely moving observer, t and tex2html_wrap_inline5257 being the time and the record of the density, respectively, kept by this observer.

Trond Hjorteland
Mon Jul 5 02:59:28 MET DST 1999