4.1. Key ingredients
At sufficiently early times the Universe is hot and dense enough that photons interact frequently and are thus tightly coupled to the Baryons. Fourier modes of the density contrast (k) in the resulting ``photon-baryon fluid'' have the following properties: On scales above the Jeans length the fluid experiences gravitational collapse. This is manifested by the presence of one growing and one decaying solution for . One can think of the growing solution corresponding to gravitational collapse and the decaying solution corresponding to the evolution of an expanding overdense region which sees its expansion slowed by gravity. During the radiation era Jeans length RJ = RH / 3 and modes ``fall inside'' RJ just as they fall inside RH. For wavelengths smaller than RJ the pressure counteracts gravity and instead of collapse the perturbations undergo oscillations, in the form of pressure (or ``acoustic'') waves. The experience of a given mode that starts outside RJ is to first experience gravitational collapse and then oscillatory behavior.
There is a later stage when the photons and Baryons decouple (which we can think of here in the instantaneous approximation). After decoupling the photons ``free stream'', interacting only gravitationally right up to the present day. The process of first undergoing collapse, followed by oscillation, is what creates the phase coherence. I will illustrate this mechanism first with a toy model.