One of the central issues of contemporary cosmology is the explanation of the origin of primordial inhomogeneities, which serve as the seeds for structure formation. Before the advent of inflationary cosmology the initial perturbations were postulated and their spectrum was designed to fit observational data. In this way practically any observation could be “explained”, or more accurately described, by arranging the appropriate initial conditions. In contrast, inflationary cosmology truly explains the origin of primordial inhomogeneities and predicts their spectrum. Thus it becomes possible to test this theory by comparing its predictions with observations.

According to cosmic inflation, primordial perturbations originated from quantum fluctuations. These fluctuations have substantial amplitudes only on scales close to the Planckian length, but during the inflationary stage they are stretched to galactic scales with nearly unchanged amplitudes. Thus, inflation links the large-scale structure of the universe to its microphysics. The resulting spectrum of inhomogeneities is not very sensitive to the details of any particular inflationary scenario and has nearly universal shape. This leads to concrete predictions for the spectrum of cosmic microwave background anisotropies.

In the previous chapter we studied gravitational instability in a universe filled with hydrodynamical matter. To understand the generation of primordial fluctuations we have to extend our analysis to the case of a scalar field condensate and quantize the cosmological perturbations. In this chapter we study the behavior of perturbations during an inflationary stage and calculate their resulting spectrum.