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
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.