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Cosmological perturbations from inflation

Matter is distributed very homogeneously and isotropically on scales larger than a few hundred Mpc. The measurements of the microwave background temperature fluctuations show that at recombination the universe was extremely homogeneous and isotropic (with accuracy ∼10−4) on all scales up to the present horizon (Spergel et al 2006 Preprint astro-ph/0603449; MacTavish et al 2005 Preprint astro-ph/0507503). On the other hand, there is a large scale structure in the observable universe and 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 (Mukhanov and Chibisov 1981 JETP Lett. 33 532; Mukhanov and Chibisov 1982 Sov. Phys.—JETP 56 258). 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.