All the modes we are interested in reenter into the Hubble radius after nucleosynthesis. Between nucleosynthesis and recombination, baryons and photons are tightly coupled because of Thomson scattering. Hence, what we are interested in is a photon-baryon "plasma" which evolves under the influence of gravity.

In this plasma, pressure, which acts as a repulsive force, competes with gravity which is an attractive force. Pressure bieng a surface effect contrarily to gravity which is a volume effect, one expects that on large scales gravity can overcome pressure, so that large scale fluctuations are unstable. This is true with non relativistic matter, but as long as baryons are coupled with photons, no instability occurs, so that plasma density fluctuation are stable. This is not the case of Dark Matter which is a non relativistic and pressureless fluid, which hence is always unstable.

Focusing on baryon-photon plasma perturbations, the crucial result coming from inflation is that before reentering into the Hubble radius, the modes are somehow "frozen" (see The "initial conditions": The predictions from inflation). As they evolve their amplitude oscillate with time. But the initial temporal phase of the mode is fixed and is the same for all the modes. Therefore, modes of different wavelength, or different frequency are initially at the same phase, and subsequently go out of phase. But the phase difference is fixed and grows linearly with time.

As a consequence, one expects that the largest modes won’t have significantly evolved at recombination, whereas smaller modes will oscillate a number of time. This is exactly what we expected to see and that we now see in the CMB anisotrpies: the power spectrum exhibits a series of peaks, which corresponds to modes which have experienced an half-integer number of oscillations, and whose amplitude is therefore maximal.

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