HI Signal from Reionization Epoch
  We investigate the all-sky signal in redshifted atomic hydrogen (HI) line from the reionization epoch. HI can be observed in both emission and absorption depending on the ratio of Lyman-$\alpha$ to ionizing flux and the spectrum of the radiation in soft xray. We also compute the signal from pre-reionization epoch and show that within the uncertainty in cosmological parameters, it is fairly robust. The main features of HI signal can be summarized as: (a) The pre-ionized HI can be seen in absorption for $\nu \simeq 10\hbox{--}40 \rm MHz$; the maximum signal strength is $\simeq 70\hbox{--}100 \rm mK$. (b) A sharp absorption feature of width $\la 5 \rm MHz$ might be observed in the frequency range $\simeq 50 \hbox{--}100 \rm MHz$, depending on the reionization history. The strength of the signal is proportional to the ratio of the Lyman-$\alpha$ and the hydrogen-ionizing flux and the spectral index of the radiation field in soft xray (c) At larger frequencies, HI is seen in emission with peak frequency between $60\hbox{--}100 \rm MHz$, depending on the ionization history of the universe; the peak strength of this signal is $\simeq 50 \rm mK$. From Fisher matrix analysis, we compute the precision with which the parameters of the model can be estimated from a future experiment: (a) the pre-reionization signal can constrain a region in the $\Omega_b h^2$--$\Omega_m h^2$ plane (b) HI observed in emission can be used to give precise, $\la 1 %$, measurement of the evolution of the ionization fraction in the universe, and (c) the transition region from absorption to emission can be used as a probe of the spectrum of ionizing sources; in particular, the HI signal in this regime can give reasonably precise measurement of the fraction of the universe heated by soft x-ray photons. 
Shiv K. Sethi