The ultimate frontier of 21cm cosmology
  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 (WF) 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 Ly$\alpha$ 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 0.01mK at $z\sim1000$, slightly larger than it would be without the WF
effect, but much weaker than previous estimates including this effect. We also
find that this signal is swamped by a smooth $1-2$ 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
$\sim 10^{-7}$ mK at $z\sim1000$. 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.
