  The process of molecule formation in the primordial gas is considered in the
framework of Friedmann cosmological models from redshift z=1e4 to z=0. First, a
comprehensive analysis of 87 gas phase reaction rates (both collisional and
radiative) relevant in the physical environment of the expanding universe is
presented and critically discussed. On this basis, calculations are carried out
of the abundance of 21 molecular species as function of redshift evaluating
consistently the molecular heating and cooling due to H2, HD and LiH molecules.
One of the major improvements of this work is the use of a better treatment of
H recombination that leads to a reduction of a factor 2-3 in the abundance of
electrons and H+ at freeze-out, with respect to previous studies. We find that
in the standard model, the residual fractional ionization at z=1 is 3.02e-4,
and the main molecular species fractional abundances H2/H=1.1e-6, HD/H2=1.1e-3,
HeH+/H=6.2e-13, LiH+/H=9.4e-18, and LiH/LiH+=7.6e-3. Finally, we provide
accurate cooling functions of H2, HD and LiH in a wide range of density and
temperature that can be conveniently used in a variety of cosmological
applications.
