This can be analyzed by adding a forcing term to our compressible fluid equations above which depends on the gravitational potential energy. If is the gas density then the full equations are where G is Newton's gravitational constant, and is the gravitational potential. A straightforward calculation shows that the growth rate of small perturbations is given by where is the initial density, and c is the speed of sound. This demonstrates that long wavelength modulations grow, and so inhomogeneities will form. A very intersting question is to understand the eventual growth of these inhomogenieties.
Observations show that the large scale structure of the universe is sheet-like.
Clearly, something else is going on as well.