We present the most detailed computation to date of the 21-cm global signal and fluctuations at $z\gtrsim 500$. Our calculations include a highly precise estimate of the Wouthuysen-Field effect and the first explicit calculation of the impact of free-free processes, the two dominant components of the signal at $z\gtrsim 800$. We implement a new high-resolution Lyman-$\alpha$ radiative transfer calculation, coupled to a state-of-the-art primordial recombination code. Using these tools, we find a global signal from 21-cm processes alone of roughly 0.01 mK at $z\sim 1000$, slightly larger than it would be without the Wouthuysen-Field effect but much weaker than previous estimates including this effect. We also find that this signal is swamped by a smooth $1–2\mathrm{mK}$ signal due to free-free absorption at high redshift by the partially ionized gas along the line of sight. In addition, we estimate the amplitude of 21-cm fluctuations, of order $\sim {10}^{-7}\mathrm{mK}$ at $z\sim 1000$. Unfortunately, we find that, due to the brightness of the low-frequency sky, these fluctuations will not be observable beyond $z\sim$ a few hundred by even extremely futuristic observations. The 21-cm fluctuations are exponentially suppressed at higher redshifts by the large free-free optical depth, making this the ultimate upper redshift limit for 21-cm surveys.

• Received 4 May 2018

DOI:https://doi.org/10.1103/PhysRevD.98.043520