Gauge ambiguity. Due to the change in density with the expansion, even a homogeneous FRW universe can appear to have a density perturbation if the time slicing is warped. The synchronous and total matter gauges choose the time slicing to correspond to the rest frame of the freely falling and total matter respectively. The Newtonian gauge chooses slicing such that the expansion rate is shear free.

Acoustic oscillations. Fluid compression through gravitational infall is resisted by photon pressure setting up acoustic oscillations. Without baryons the photon blueshift on infall is equal and opposite to the redshift upon leaving the potential leading to symmetric oscillations around zero with a Doppler effect of equal magnitude but 90 degrees out of phase. Baryons increase the mass of the fluid causing more infall and a net zero point displacement. Temperature crests (compression) are enhanced over troughs (rarefaction) and velocity contributions.

Baryon Drag. Baryons drag the photons into potential wells leading to a zero point displacement of $|R\Psi|$ and alternating peak heights in the rms fluctuation which provide a measure of $\Omega_b h^2$. The fall off near $a_*$ of the amplitude is due to diffusion damping.