The CMBR fluctuations from HI perturbations prior to reionization
  Loeb and Zaldarriaga (2003) have recently proposed that observations of the CMBR brightness temperature fluctuations produced by the HI inhomogeneities prior to reionization hold the promise of probing the primordial power spectrum to a hitherto unprecedented level of accuracy. This requires a precise quantification of the relation between density perturbations and brightness temperature fluctuations. Brightness temperature fluctuations arise from two sources (1.) fluctuations in the spin temperature, and (2.) fluctuations in the HI optical depth, both of which are caused by density perturbations. For the spin temperature, we investigate in detail its evolution in the presence of HI fluctuations. For the optical depth, we find that it is affected by density perturbations both directly and through peculiar velocities which move the absorption features around in frequency. The latter effect, which has not been included in earlier studies, is similar to the redshift space distortion seen in galaxy surveys and this can cause changes of 50% or more in the birghtness temperature fluctuations. 
Somnath Bharadwaj and Sk. Saiyad Ali