In this hypothesis, what is the fate of the gas, and when do the cold gas clumps form? After recombination (z ~ 1500), the largest masses to get non-linear are of M ~ 106 - 8 M, and the Jeans mass is M ~ 105 M(b / 0.06)-1/2 (h / 0.5)-1. All masses between these two will collapse and decouple from expansion, but the structures at precisely the Jeans mass collapse first. The masses correspond to typical z = 0 giant molecular clouds. If cooling is efficient enough (cool ~ ff), the collapse is quasi-isothermal, and fragmentation occurs, since the Jeans mass becomes smaller and smaller as the density increases (e.g., Hoyle 1953). Fragmentation is limited by opacity, and the smallest fragments (or clumpuscules), which are at the transition of being pressure supported, are today of the order of 10-3 M, and their mass grows slowly, as T1/4 or (1 + z)1/4, with redshift.
Cooling might be a problem, since primordial gas is non-metallic, with no dust grains; above 104K the main coolant is atomic hydrogen (by collisional excitation of Ly), then vibration-rotation lines of molecular hydrogen take over until T = 200K, because a significant quantity of H2 molecules forms through H- and H2+. Below 200K, HD is then more efficient. Many groups have computed the physico-chemistry of the primordial gas, to determine the size of the first forming bound structures (Yoneyama 1972; Hutchins 1976; Carlberg 1981; Palla et al. 1983; Lepp & Shull 1984). All of them have found that the cooling is indeed efficient, as soon as the redshift is below z ~ 200.
We have studied in particular the recursive formation of fragments, as expected in a fractal structure of dimension D = 1.7 (which fixes the density as a function of sizes and masses). Cooling in such a fractal is very efficient, as shown by the temperature curve, which quickly returns back to TCMB of the background after virialisation (cf fig. 2). Very soon, the clumps are almost entirely molecular (Combes & Pfenniger 1998).
Figure 2. Evolution of temperature (T6 in 106K), molecular fraction (fH2), ionization fraction (xe) and density (n3 in 103cm-3) for a gas cloud after recombination, collapsing at zvir = 100, with h = 0.5, = 1 and b = 0.06 (from Combes & Pfenniger 1998).