Primordial non-gaussianity from the bispectrum of 21-cm fluctuations in the dark ages

A measurement of primordial non-Gaussianity will be of paramount importance to distinguish between different models of inflation. Cosmic microwave background (CMB) anisotropy observations have set unprecedented bounds on the non-Gaussianity parameter f(NL) but the interesting regime f(NL) less than or similar to 1 is beyond their reach. Brightness-temperature fluctuations in the 21-cm line during the dark ages (z similar to 30-100) are a promising successor to CMB studies, giving access to a much larger number of modes. They are, however, intrinsically nonlinear, which results in secondary non-gaussianities orders of magnitude larger than the sought-after primordial signal. In this paper we carefully compute the primary and secondary bispectra of 21-cm fluctuations on small scales. We use the flat-sky formalism, which greatly simplifies the analysis, while still being very accurate on small angular scales. We show that the secondary bispectrum is highly degenerate with the primordial one, and argue that even percent-level uncertainties in the amplitude of the former lead to a bias of order Delta f(NL) similar to 10. To tackle this problem we carry out a detailed Fisher analysis, marginalizing over the amplitudes of a few smooth redshift-dependent coefficients characterizing the secondary bispectrum. We find that the signal-to-noise ratio for a single redshift slice is reduced by a factor of similar to 5 in comparison to a case without secondary non-gaussianities. Setting aside foreground contamination, we forecast that a cosmic-variance-limited experiment observing 21-cm fluctuations over 30 <= z <= 100 with a 0.1-MHz bandwidth and 0.1 arc min angular resolution could achieve a sensitivity of order f(NL)(local) similar to 0.03, f(NL)(equil) similar to 0.04 and f(NL)(ortho) similar to 0.03.