In this chapter, we describe one ultimate consequence of the evolution of the primordial perturbation, namely the observable matter distribution in the Universe. It is not our intention to provide a detailed account of how observers probe the matter distribution, something which is now carried out with impressive precision. Instead, we focus on the outcome of those observations and their comparison with theory. We will explain the fundamental theoretical strategy, and highlight some simple physical arguments which account for the broad features of the data.

To use linear perturbation theory after galaxies begin to form we need to smooth the density contrast as described in Section 5.1.2. After looking in more detail at the description of smoothing, we will see in a qualitative way how the theory describes ‘bottom-up’ structure formation. We go on to give a more quantitative description, which applies to the formation of objects with a given mass as long as they are rare. In this way we obtain an estimate of the abundance of such objects, which may be compared with observation.

Next we come to the issue of comparing the calculated density perturbation directly with observation. More precisely, we seek to compare with observation the spectrum of the density contrast, and higher correlators which may signal nongaussianity. For this purpose we have to remember that the galaxy number density won't precisely trace the matter density, since the latter includes dark matter (both baryonic and cold dark matter (CDM)).