The Dark Ages' 21-cm Trispectrum
  We investigate tomography of 21-cm brightness temperature fluctuations during
the Dark Ages as a probe for constraining primordial non-Gaussianity. We expand
the 21- cm brightness temperature up to cubic order in perturbation theory and
improve previous models of the signal by including the effect of the free
electron fraction. Using modified standard perturbation theory methods that
include baryonic pressure effects we derive an improved secondary bispectrum
and for the first time derive the secondary trispectrum of 21-cm brightness
temperature fluctuations. We then forecast the amount of information available
from the Dark Ages to constrain primordial non-Gaussianity, including the
imprints of massive particle exchange during inflation and we determine how
much signal is lost due to secondary non-Gaussianity. We find that although
secondary non-Gaussianity swamps the primordial signal, primordial
non-Gaussianity can still be extracted with signal-to-noise ratios that surpass
current and future CMB experiments by several orders of magnitude, depending on
the experimental setup. Furthermore, we conclude that for the bi- and
trispectra of massive particle exchange marginalizing over other primordial
shapes affects signal-to-noise ratios more severely than secondary shapes.
Baryonic pressure effects turn out to have a negligible impact on our
forecasts, even at scales close to the Jeans scale. The results of this work
reinforce the prospects of 21-cm brightness temperature fluctuations from the
Dark Ages as the ultimate probe for primordial non-Gaussianity.
