  We investigate the early formation of bound objects with masses comparable to
the cosmological Jeans mass (10^5 solar masses). We follow the growth of
isolated spherically symmetric density peaks starting from the linear
perturbative regime. The initial parameters correspond to density peaks of
various widths and heights in a Cold Dark Matter cosmology. We use a
one-dimensional spherical Lagrangian hydrodynamics code to follow the
dynamical, thermal, and non-equilibrium chemical evolution of the gas. The
system includes a collisionless dark matter component and a baryonic component
composed of the nine species H, H^-, H^+, He, He^+, He^{++}, H_2, H_2^+, and
e^-. All relevant chemical reactions between these species and their cooling
mechanisms are included in the calculations. We find that radiative cooling by
H_2 affects the collapse dynamics of the gas only after it has already
virialized and become part of the bound object. Therefore, radiative cooling is
unlikely to have triggered the initial collapse of perturbations at redshifts
z>10. Nevertheless, objects with baryonic masses well below the linear-theory
Jeans mass (<10^3 solar masses) collapse due to shell crossing by the dark
matter. Such objects could be the progenitors of a primordial population of
high-mass stars in the intergalactic medium.
