The Infancy of Cosmic Reionization
  We consider the early stages of cosmic hydrogen or helium reionization, when ionizing sources were still rare. We show that Poisson fluctuations in the galaxy distribution substantially affected the early bubble size distribution, although galaxy clustering was also an essential factor even at the earliest times. We find that even at high redshifts, a significant fraction of the ionized volume resided in bubbles containing multiple sources, regardless of the ionizing efficiency of sources or of the reionization redshift. In particular, for helium reionization by quasars, one-source bubbles last dominated (i.e., contained 90% of the ionized volume) at some redshift above z=7.3, and hydrogen reionization by stars achieved this milestone at z>23. For the early generations of atomic-cooling halos or molecular-hydrogen-cooling halos, one-source ionized regions dominated the ionized volume only at z>31 and z>48, respectively. To arrive at these results we develop a statistical model for the effect of density correlations and discrete sources on reionization and solve it with a Monte Carlo method. 
Rennan Barkana (1, 2, 3) ((1) University of Tokyo, (2) Caltech, (3)   Tel Aviv University)