  We show that various milestones of high-redshift galaxy formation, such as
the formation of the first stars or the complete reionization of the
intergalactic medium, occurred at different times in different regions of the
universe. The predicted spread in redshift, caused by large-scale fluctuations
in the number density of galaxies, is at least an order of magnitude larger
than previous expectations that argued for a sharp end to reionization. This
cosmic scatter in the abundance of galaxies introduces new features that affect
the nature of reionization and the expectations for future probes of
reionization, and may help explain the present properties of dwarf galaxies in
different environments. The predictions can be tested by future numerical
simulations and may be verified by upcoming observations. Current simulations,
limited to relatively small volumes and periodic boundary conditions, largely
omit cosmic scatter and its consequences. In particular, they artificially
produce a sudden end to reionization, and they underestimate the number of
galaxies by up to an order of magnitude at redshift 20.

Astrophysics