University of Chicago

We know that the universe has been ionized at least until *z = 5 *from
the null detection of the Gunn-Peterson effect. Hence after standard recombination
at *z = 1000 *, the universe must have underwent reionization. However,
the amount of rescattering of CMB photons is negligible unless the ionization
persists through redshifts of several tens. This is unlikely in models
without excessive small scale power and in such models, e.g. scale invariant
adiabatic ones, degree scale anisotropy detections
are already severely constraining the amount of reionization allowable.
Still, it is useful to recall the basic physical effects associated with
reionization.

*Figure: *Reionization Effects from
Hu & White (1995)

*Rescattering Damping: *Rescattering
damps fluctuations in the same manner as diffusion. Scattering eliminates
anisotropies leaving them only in the unscattered fraction exp(-optical
depth). Since outside the horizon, streaming
has not yet converted temperature fluctuations to anisotropies, power is
only lost below the horizon at the rescattering epoch.

*Doppler Effect: *Diffusion and rescattering
prevents the appearance of large temperature fluctuations. However, the
Doppler effect from scattering off electrons caught in the gravitational
instability of the baryons can regenerate anisotropies. These contributions
are suppressed in the same way as the late ISW effect:

*Figure: *Cancelled Doppler Effect
from Hu (1995)

Photons that last scattered off opposite sides of the perturbation get Doppler shifted by equal and opposite amounts. Thus for wavelengths far below the thickness of the last scattering surface, Doppler contributions tend to cancel leaving a negligible net effect.

*Non-linear Effects: *At very small
scales, higher order contributions are more efficient than the Doppler
effect in regenerating anisotropies. These generally make use of combining
the Doppler effect with variations in the optical depth. For example, the
enhanced baryon density in an overdense region leads to preferential scattering
in those regions. If the perturbations are also caught up in a bulk flow,
then a Doppler shift arises that can escape cancellation (known as the
Vishiac or Ostriker-Vishniac effect):

*Figure: *Vishniac Mechanism from
Hu (1995)

Similarly, inhomogeneities in the ionization fraction, or contributions from clusters (kinematic Sunyaev-Zel'dovich effect) can give Doppler contributions. Clusters can also produce anisotropic spectral distortions due to the upscattering in frequency of photons by hot electrons (thermal Sunyaev-Zel'dovich effect).

Again, in models without high amplitude small-scale power, it is unlikely that any of these effects will dominate the total anisotropy in the observable regime.