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 
Mpc (comparably, the size of the observable Universe is about
3000 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 ( 
Mpc). These density fluctuations where present
at the decoupling of matter and radiation at redshift 
. 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 
. The mass density is then
where 
is the mean background mass density. Note that the spatial
coordinates 
are comoving; i.e. expanding with the model. One can imagine that
is the coordinates of a freely moving observer, t and 
being the time and the record of the density, respectively, kept by this observer.
