As we have summarized above, irregularities in the distribution of matter have been detected on scales up to 30 h-1 Mpc, corresponding to 1% of the present day horizon size, but on larger scales the Universe appears to be homogeneous and isotropic. Clearly these observations pose a fundamental question. Why is the Universe nearly but not quite homogeneous and isotropic?
There have been several different views on this issue. On the one hand, it may be argued that the Friedmann models require such precise initial conditions as to render them unlikely, a more natural initial state would be one of primordial chaos (Misner, 1968; Rees, 1972). Of course, with this view it is necessary to demonstrate that a chaotic model will naturally evolve towards the Friedmann solution at late times. It has been argued (e.g. Peebles, 1980a) that such a program is unlikely to be successful. Indeed, some authors have reversed the argument, using the present state of the Universe to set stringent limits on how chaotic the early Universe could have been (Barrow and Matzner, 1977). The alternative view is that the early Universe was close to Friedmannian at early times, but that small irregularities grew by gravitational instability, ultimately forming the galaxies and clusters that we now observe. In this Section we present a summary of the relativistic theory, which is necessary in order to study the evolution of small perturbations on spatial scales larger than the instantaneous particle horizon. Detailed treatments have been presented by Harrison (1967), Weinberg (1972), Press and Vishniac (1980a) and Peebles (1980a) but here we will follow closely the approach of Bardeen (1980).