Growth of linear perturbations before the era of the first galaxies

We calculate the evolution of linear density and temperature perturbations in a universe with dark matter, baryons and radiation, from cosmic recombination until the epoch of the first galaxies. In addition to gravity, the perturbations are affected by electron scattering with the radiation, by radiation pressure and by gas pressure. We include the effect of spatial fluctuations in the baryonic sound speed and show that they induce a 10 per cent change in the baryonic density power spectrum on small scales, and a larger change on all scales in the power spectrum of gas temperature fluctuations. A precise calculation of the growth of linear perturbations is essential because they provide the initial conditions for the formation of galaxies and they can also be probed directly via cosmological 21-cm fluctuations. We also show that in general the thermal history of the cosmic gas can be measured from 21-cm fluctuations using a small-scale anisotropic cut-off due to the thermal width of the 21-cm line.