**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 *R*_{J} =
*R*_{H} / 3 and
modes ``fall inside''
*R*_{J} just as they fall inside *R*_{H}. For
wavelengths smaller than
*R*_{J} 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
*R*_{J} 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.