**1.1. Intergalactic Hydrogen Density**

The proper mean density of hydrogen nuclei at redshift *z* may be
expressed in standard cosmological terms as:

(1) | |

(2) |

where *Y* is the primordial He abundance by mass,
_{crit} = 3*H*_{0}^{2}
/ (8 *G*) is the critical density,
_{b} =
_{b} /
_{crit} is the
current baryonic density parameter, and *H*_{0} = 100
*h* km s^{-1} Mpc^{-1} is the
present-day
Hubble constant. Standard nucleosynthesis models together with recent
observations of
Deuterium yield *Y* = 0.247 ± 0.02, and
_{b}
*h*^{2} = 0.0193 ± 0.0014. Thus,

As some of the baryons had already collapsed into galaxies at *z* =
2-5, the
value of _{b}
*h*^{2} = 0.019 should strictly be considered as an upper
limit to the intergalactic density parameter.

Because of the overwhelming abundance of hydrogen, the ionization of
this element is of great importance for determining the physical state of the
IGM. Popular cosmological models predict that most of the intergalactic
hydrogen
was reionized by the first generation of stars or quasars at *z* = 7-15.
The case that has received the most theoretical studies is one where
hydrogen is ionized by the absorption of photons, *H* +
-> *p + e*
(as opposite to collisional ionization *H + e* -> *p + e + e*)
shortward of
912 Å; that is, with energies exceeding 13.6 eV, the energy of the
Lyman edge. The
process of reionization began as individual sources started to generate
expanding H II regions in the surrounding IGM; throughout an H II region, H is
ionized and He is either singly or doubly ionized. As more and more sources of
ultraviolet radiation switched on, the ionized volume grew in size. The
reionization ended when the cosmological H II regions overlapped and filled
the intergalactic space.