2.3. Passive vs. active perturbations

Perturbations can be passive (i.e. primordial) or active. Passive perturbations are those which are generated in the very early Universe (e.g. during inflation), and henceforth evolve passively, being changed only by the action of cosmic expansion and gravity. This means that the phases of such perturbations, in a Fourier expansion of the density field, will remain constant once the perturbations are generated, and as long as they evolve linearly. Therefore, if one adds them up over time, they add up coherently. It is in this sense that passive perturbations are usually also called coherent. Further, as soon as these perturbations enter the particle horizon, the photon-baryon fluid will try to flow into the potential wells associated with the perturbations, setting in motion acoustic oscillations in the fluid which will be in in phase. Primordial perturbations, adiabatic or isocurvature, always lead to such in-phase (or coherent) acoustic oscillations of the photon-baryon fluid.

On the contrary, (random) active perturbations, because they are constantly being produced randomly across space, tend to produce an ensemble of perturbations whose phases will add up over time incoherently. Such perturbations necessarily lead to oscillations of the photon-baryon fluid which will be out-of-phase with each other, with the result that their effects will cancel themselves out. Active perturbations, like those produced by standard topological defect models, lead in general to incoherent acoustic oscillations in the photon-baryon fluid (though in a few models some coherence can temporarily exist on scales that have just entered the Hubble radius), as they are generated almost completely at random. However, active perturbations are not necessarily produced in such a way. Models of active perturbations have been proposed, though in a somewhat contrived manner, which seem to be able to produce perfectly coherent oscillations in the photon-baryon fluid, analogous to those produced by passive perturbations [see e.g. (76)]. However, clearly, the discovery that the photon-baryon fluid that existed before decoupling had coherent acoustic oscillations, would strongly boost the status of inflation as the best available explanation for the formation of structure.

In terms of large-scale structure, these oscillations only leave a detectable signature in the power spectrum of density perturbations if baryons comprise in excess of about 15 per cent of the total matter content in the Universe (61). The main problem is that non-linear evolution of the power spectrum washes out the signature of the baryon induced oscillations for large k, where the power spectrum can be better determined observationally, leaving out basically only the two peaks on the largest scales as a smoking gun, where observational errors are larger due to cosmic variance.