The spin temperature of neutral hydrogen during cosmic pre-reionization
  We re-examine the role of collisions in decoupling the HI 21-cm spin temperature from the cosmic microwave background (CMB). The cross section for de-exciting the 21-cm trasition in collisions with free electrons is more than 10 times larger than it is in collisions with other atoms. If the fraction of free electrons in the diffuse cosmic gas is between 10 and 30 per cent then collisions alone can decouple the spin temperature from the cosmic microwave background (CMB), even in moderately under-dense regions at z >15. This decoupling is especially important during the very early stages of re-ionization when a Ly-alpha continuum background had yet to be established. As a detailed example, we develop a semi-analytic model to quantify 21-cm emission signatures from a diffuse gas which is partially ionized at z>10 by an X-ray background. We find 21-cm differential brightness temperature fluctuations with a mean of ~8 mK and a rms value as large as 5 mK, for a frequency resolution bandwidth of 100 KHz and a beamsize of 3 arcmin. Another example where free electron-atom collisions are important is during the recombination of bubbles ionized by short-lived UV sources. When the ionized fraction in these bubbles drops to 10-20 per cent their differential temperature can be as high as 10 mK. We also consider the correlation of the 21-cm temperature as a function of frequency. By isotropy, a comparison with the angular projected correlation in the plane of the sky should yield an estimate for the matter density parameter, Omega_m, and the dark energy component. This variant of the Alcock-Paczyski test is applicable for any reionization scenario. 
Adi Nusser