Measuring the Small-Scale Power Spectrum of Cosmic Density Fluctuations through 21 cm Tomography Prior to the Epoch of Structure Formation

The thermal evolution of the cosmic gas decoupled from that of the cosmic microwave background (CMB) at a redshift $z\sim 200$. Afterwards and before the first stars had formed, the cosmic neutral hydrogen absorbed the CMB flux at its resonant 21 cm spin-flip transition. We calculate the evolution of the spin temperature for this transition and the resulting anisotropies that are imprinted on the CMB sky due to linear density fluctuations during this epoch. These anisotropies, at an observed wavelength of $10.56[(1+z)/50]\mathrm{m}$, contain an amount of information that is orders of magnitude larger than any other cosmological probe.