In this chapter, we put together a set of observations presently available to us (i.e., in 1999), which can be interpreted using the linear and quasi-linear approaches that we have described. At present, no single type of observation is dominant in providing constraints on models of structure formation; instead, the best results come from compiling as wide a set of data as possible, covering a range of scales from our present observable Universe down to the scales of galaxies.

No doubt, the observational details will be superseded quickly, but the general approaches to using them are well established. We also give this discussion here as a post hoc motivation for the models that we considered earlier, both the inflationary aspects and the structure formation scenarios.

A detailed comparison of models with observations requires numerical investigation, to probe the nonlinear regime where many of the observations of galaxy correlations and velocities are made. However, we have seen that there remain a very significant number of undetermined parameters on which the formation of structure depends; we might consider three inflationary parameters, δH, n, and r, and several cosmological parameters such as h, Ω0, ∧, Ωb, a possible admixture of hot dark matter ΩHDM, and the redshift of reionization Zion. In all the models that we discuss, we need cold dark matter (CDM); inflation-based models do not appear to work without it. It always has whatever density is required to make the total add up correctly.