  We investigate the suppression of the baryon density fluctuations compared to
the dark matter in the linear regime. Previous calculations predict that the
suppression occurs up to a characteristic mass scale of ~ 1,000,000 solar
masses, which suggests that pressure has a central role in determining the
properties of the first luminous objects at early times. We show that the
expected characteristic mass scale is in fact substantially lower (by a factor
of ~ 3-10, depending on redshift), and thus the effect of baryonic pressure on
the formation of galaxies up to reionization is only moderate. This result is
due to the influence on perturbation growth of the high pressure that prevailed
in the period from cosmic recombination to z ~ 200, when the gas began to cool
adiabatically and the pressure then dropped. At z ~ 10 the suppression of the
baryon fluctuations is still sensitive to the history of pressure in this
high-redshift era. We calculate the fraction of the cosmic gas that is in
minihalos and find that it is substantially higher than would be expected with
the previously-estimated characteristic mass. Expanding our investigation to
the non-linear regime, we calculate in detail the spherical collapse of
high-redshift objects in a Lambda-CDM universe. We include the gravitational
contributions of the baryons and radiation and the memory of their kinematic
coupling before recombination. We use our results to predict a more accurate
halo mass function as a function of redshift.
