4.4. Reionization and generation of secondary fluctuations

It is not implausible that isothermal fluctuations formed bound systems at an early epoch (e.g. Peebles and Dicke, 1968). Sufficient early star formation would have reionized the universe. If the electron scattering optical depth to redshift z is , then reionization must occur at

(4.24)

where x is the fractional ionization (assumed constant oncc reionization occurs). Reionization at redshift z requires a modest energy input in ionizing photons, amounting to

(4.25)

This is only a small fraction of the energy that is potentially available in an early generation of stars: for example, nucleosynthesis in a fraction F of the baryonic mass of the universe releases ~ 10⁵(F / 0.01) eV per nucleon. However the binding energy release in forming galaxy groups and clusters does not suffice to produce significant ionization at z > 10.

If reionization occurs at z > 10, then much of the small-scale radiation anisotropy is destroyed. On angular scales 5( x)^1/3 degrees, however, reionization does not affect the residual radiation anisotropy. One can effectively see back to the decoupling epoch on large angular scales, since there has not been time for these scales to have undergone any causal interaction and smoothing at z > 10 where the last scatterings occurred.

Even on smaller angular scales, secondary fluctuations are produced. These arise because the large-scale density fluctuations drive velocity fluctuations on the surface of last scattering. However the amplitudes of the expected temperature fluctuations are reduced by about an order of magnitude relative to those predicted in the absence of reionization.