Until now we have implicitly assumed that the
evolution of the perturbations plays a small role as is generally
true
for scales larger than the horizon at last scattering.
Evolution plays an important role for
small-scale scalar perturbations where there is enough
time for sound to cross the perturbation before last scattering.
The infall of the photon fluid into troughs compresses the fluid, increasing
its density and temperature. For adiabatic fluctuations,
this compression reverses the sign of the effective temperature
perturbation when the sound horizon s grows to be 
(see Fig. 13a).
This reverses the sign of the correlation with the quadrupole moment.
Infall continues until the compression is so great that photon pressure
reverses the flow when 
. Again the correlation reverses sign.
This pattern of correlations and anticorrelations continues
at twice the frequency of the acoustic oscillations themselves
(see Fig. 13a).
Of course the polarization is only generated at last scattering
so the correlations and anticorrelations are a function of
scale with sign changes at multiples of 
, where
is the sound horizon at last scattering. As discussed
in §3.2, these fluctuations project onto
anisotropies as 
.
Any scalar fluctuation will obey a similar pattern that reflects
the acoustic motions of the photon fluid. In particular, at the
largest scales the 
, the polarization must
be anticorrelated with the temperature because the fluid will
always flow with the temperature gradient initially from hot to cold.
However, where the sign reversals occur depend on the
acoustic dynamics and so is a useful probe of the nature of
the scalar perturbations, e.g. whether they are adiabatic or
isocurvature ([Hu & White] 1996). In typical isocurvature models, the lack of
initial temperature perturbations delays the acoustic
oscillation by 
in phase
so that correlations reverse at 
(see Fig. 13b).
For the vector and tensor modes, strong evolution can introduce a small correlation with temperature fluctuations generated after last scattering. The effect is generally weak and model dependent and so we shall not consider it further here.
