Perturbations

Abstract

The perturbations of a FLRW universe are extremely important because they leave an imprint as temperature fluctuations in the cosmic microwave background, which have been detected by the COBE mission in 1992 [809]. These perturbations are the subject of intense experimental study. Hence, density and gravitational wave fluctuations around the FLRW background provide the means to test the predictions of theories of the early universe. Soon after the introduction of the idea of inflation in cosmology, it was realized that in addition to solving the horizon, flatness, and monopole problems, inflation provides the extra advantage of a natural mechanism to generate density perturbations. Such a mechanism is missing in the standard big bang model, where an initial spectrum of perturbations has to be assumed ad hoc. Instead, during inflation, quantum fluctuations of the inflaton field provide the required density perturbations. Their physical wavelengths λ_phys = aλ (where A is the comoving wavelength) scale as the scale factor a, while the horizon size H^-1 stays almost constant during inflation. As a consequence, perturbations cross outside the horizon during inflation. The spectrum of density perturbations is usually specified by their amplitude at this horizon crossing.