The first galaxies to appear in the universe at redshifts z>20 created
ionized bubbles in the intergalactic medium of neutral hydrogen left over from
the Big-Bang. It is thought that the ionized bubbles grew with time, surrounded
clusters of dwarf galaxies and eventually overlapped quickly throughout the
universe over a narrow redshift interval near z~6. This event signaled the end
of the reionization epoch when the universe was a billion years old. Measuring
the hitherto unknown size distribution of the bubbles at their final overlap
phase is a focus of forthcoming observational programs aimed at highly
redshifted 21cm emission from atomic hydrogen. Here we show that the combined
constraints of cosmic variance and causality imply an observed bubble size at
the end of the overlap epoch of ~10 physical Mpc, and a scatter in the observed
redshift of overlap along different lines-of-sight of ~0.15. This scatter is
consistent with observational constraints from recent spectroscopic data on the
farthest known quasars. Our novel result implies that future radio experiments
should be tuned to a characteristic angular scale of ~0.5 degrees and have a
minimum frequency band-width of ~8 MHz for an optimal detection of 21cm flux
fluctuations near the end of reionization.Comment: Accepted for publication in Nature. Press embargo until publishe