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In concordance cosmology, dark matter density perturbations generated byinflation lead to nonlinear, virialized minihalos, into which baryons collapseat redshift $z \sim 20$. We survey here novel baryon evolution produced by amodification of the power spectrum from white noise density perturbations atscales below $k \sim 10 h {Mpc}^{-1}$ (the smallest scales currently measuredwith the Lyman-$\alpha$ forest). Exotic dark matter dynamics, such as wouldarise from scalar dark matter with a late phase transition (similar to anaxion, but with lower mass), create such an amplification of small scale power.The dark matter produced in such a phase transition collapses into minihalos,with a size given by the dark matter mass within the horizon at the phasetransition. If the mass of the initial minihalos is larger than $\sim 10^{-3}M_\odot$, the modified power spectrum is found to cause widespread baryoncollapse earlier than standard $\Lambda$CDM, leading to earlier gas heating. Italso results in higher spin temperature of the baryons in the 21 cm linerelative to $\Lambda$CDM at redshifts $z > 20$ if the mass of the minihalo islarger than $1 M_\odot$. It is estimated that experiments probing 21 cmradiation at high redshift will contribute a significant constraint on darkmatter models of this type for initial minihalos larger than $\sim 10 M_\odot$.Early experiments reaching to $z\approx 15$ will constrain minihalos down to$\sim 10^3 M_\odot$.Comment: 8 pages, 9 figure

White noise from dark matter: 21 cm observations of early baryon collapse