Fluctuations of the 21 cm brightness temperature before the formation of the first stars hold the promise of becoming a high-precision cosmological probe in the future. The growth of overdensities is very well described by perturbation theory at that epoch, and the signal can in principle be predicted to arbitrary accuracy for given cosmological parameters. Recently, Tseliakhovich and Hirata pointed out a previously neglected and important physical effect, due to the fact that baryons and cold dark matter (CDM) have supersonic relative velocities after recombination. This relative velocity suppresses the growth of matter fluctuations on scales $k\sim 10–{10}^3{\mathrm{Mpc}}^{-1}$. In addition, the amplitude of the small-scale power spectrum is modulated on the large scales over which the relative velocity varies, corresponding to $k\sim 0.005–1{\mathrm{Mpc}}^{-1}$. In this paper, the effect of the relative velocity on 21 cm brightness temperature fluctuations from redshifts $z\ge 30$ is computed. We show that the 21 cm power spectrum is affected on most scales. On small scales, the signal is typically suppressed several tens of percent, except for extremely small scales ($k\gtrsim 2000{\mathrm{Mpc}}^{-1}$) for which the fluctuations are boosted by resonant excitation of acoustic waves. On large scales, 21 cm fluctuations are enhanced due to the nonlinear dependence of the brightness temperature on the underlying gas density and temperature. The enhancement of the 21 cm power spectrum is of a few percent at $k\sim 0.1{\mathrm{Mpc}}^{-1}$ and up to tens of percent at $k\lesssim 0.005{\mathrm{Mpc}}^{-1}$, for standard $\mathrm{\Lambda }\mathrm{CDM}$ cosmology. In principle this effect allows one to probe the small-scale matter power spectrum not only through a measurement of small angular scales but also through its effect on large angular scales.

• Received 8 January 2014

DOI:https://doi.org/10.1103/PhysRevD.89.083506