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.