2.2. The initial conditions
The idea that galaxies and other cosmic structures are the result of the slow amplification by the force of gravity of small primordial perturbations present in the mass density at early times goes back, at least, to the 1940s (Lifshitz 1946). However, it was only in the early 1980s that a physical mechanism capable of producing small perturbations was identified. This is the mechanism of inflation, an idea due to Guth (1981), which changed the face of modern cosmology. Inflation is produced by the dominant presence of a quantum scalar field which rolls slowly from a false to the true vacuum, maintaining its energy density approximately constant and causing the early Universe to expand exponentially for a brief period of time. Quantum fluctuations in the inflaton field are blown up to macroscopic scales and become established as genuine adiabatic ripples in the energy density. Simple models of inflation predict the general properties of the resulting fluctuation field: it has Gaussian distributed amplitudes and a near scale-invariant power spectrum (Starobinskii 1982).
After three decades of ever more sensitive searches, evidence for the presence of small fluctuations in the early universe was finally obtained in 1992. Since prior to recombination the matter and radiation fields were coupled, fluctuations in the mass density are reflected in the temperature of the radiation. Temperature fluctuations in the CMB were discovered by the COBE satellite (Smoot et al. 1992) and are now being measured with ever increasing accuracy, particularly by detectors deployed in long-flight balloons (de Bernardis et al. 2000, Hanany et al. 2000, Leitch et al. 2002). The spectrum of temperature fluctuations is just what inflation predicts: it is scale invariant on large scales and shows a series of "Doppler" or "acoustic" peaks which are the result of coherent acoustic oscillations experienced by the photon-baryon fluid before recombination. The characteristics of these peaks depend on the values of the cosmological parameters. For example, the location of the first peak is primarily determined by the large-scale geometry of the Universe and thus by the value of . Current data imply a flat geometry, consistent with eqn. 2.1.
The spectrum of primordial fluctuations generated, for example, by inflation evolves with time in a manner that depends on the content of the Universe and the values of the cosmological parameters. The dark matter acts as a sort of filter, inhibiting the growth of certain wavelengths and promoting the growth of others. Following the classical work of Bardeen et al. (1986), transfer functions for different kinds of dark matter (and different types of primordial fluctuation fields, including non-Gaussian cases) have been computed. In Gaussian models, the product (in Fourier space) of the primordial spectrum and the transfer function, together with the growing mode of the associated velocity field, provides the initial conditions for the formation of cosmic structure.