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We study the formation of molecular hydrogen, after the epoch ofre-ionization, in the context of canonical galaxy formation theory due tohierarchical clustering. There is an initial epoch of $H_2$ production in thegas phase through the $H^-$ route which ends at a redshift of order unity. Starformation in the protogalactic disks can become self-regulated. The processresponsible for the feedback is heating of the gas by the internal stellarradiation field which can dominate the background radiation field at variousepochs. It is possible to define a maximum star formation rate during thisepoch. Plausible estimates give a rate of 0.2-2 Mo yr-1 for condensationscorresponding to 1 sigma and 2 sigma initial density fluctuations. Therefore,the production of metals and dust proceeds slowly in this phase. This moderateepoch is terminated by a phase transition to a cold dense and warmneutral/ionized medium once the metals and dust have increased to a levelZ=0.03-0.1 Z_o. Then: (1) atoms and molecules such as C, O and CO becomeabundant and cool the gas to below $300 K$ ; (2) the dust abundance has becomesufficiently high to allow shielding of the molecular gas and; (3) molecularhydrogen formation can occur rapidly on grain surfaces. This phase transitionoccurs at a redshift of approximately 1.5, with a fiducial range of 1.2<z<2.The combination of feedback and a phase transition provides a naturalresolution of the G-dwarf problem.Comment: 33 pages LaTeX, 5 PS figures, uses aasms.sty file, Accepted by Ap

Molecules at High Redshift: The Evolution of the Cool Phase of Protogalactic Disks