Using our cosmological radiative transfer code , we study the implications of the updated quasi-stellar object ( 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 \sim 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 \geq 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 .