  Using our cosmological radiative transfer code, we study the implications of
the updated QSO emissivity and star formation history for the escape fraction
(f_esc) of hydrogen ionizing photons from galaxies. We estimate the f_esc that
is required to reionize the Universe and to maintain the ionization state of
the intergalactic medium in the post-reionization era. At z>5.5, we show that a
constant f_esc of 0.14 to 0.22 is sufficient to reionize the Universe. At
z<3.5, consistent with various observations, we find that f_esc can have values
from 0 to 0.05. However, a steep rise in f_esc, of at least a factor of ~3, is
required between z=3.5 to 5.5. It results from a rapidly decreasing QSO
emissivity at z>3 together with a nearly constant measured H I photoionization
rates at 3<z<5. We show that, this requirement of a steep rise in f_esc over a
very short time can be relaxed if we consider the contribution from a recently
found large number density of faint QSOs at z>4. In addition, a simple
extrapolation of the contribution of such QSOs to high-z suggests that QSOs
alone can reionize the Universe. This implies, at z>3.5, that either the
properties of galaxies should evolve rapidly to increase the f_esc or most of
the low-mass galaxies should host massive black holes and sustain accretion
over a prolonged period. These results motivate a careful investigation of
theoretical predictions of these alternate scenarios that can be distinguished
using future observations. Moreover, it is also very important to revisit the
measurements of H I photoionization rates that are crucial to the analysis
presented here.
