The Bispectrum of Redshifted 21-cm Fluctuations from the Dark Ages

Brightness temperature fluctuations in the redshifted 21 cm background from the cosmic dark ages are generated by irregularities in the gas density distribution and can thus be used to determine the statistical properties of density fluctuations in the early universe. Here we derive the most general expansion of brightness temperature fluctuations up to second order in terms of all the possible sources of spatial fluctuations. We then focus on the three-point statistics and compute the angular bispectrum of brightness temperature fluctuations generated prior to the epoch of hydrogen reionization. For simplicity, we neglect redshift-space distortions. We find that low-frequency radio experiments with arcminute angular resolution can easily detect non-Gaussianity produced by nonlinear gravity, with high signal-to-noise ratio. The bispectrum thus provides a unique test of the gravitational instability scenario for structure formation and can be used to measure the cosmological parameters. Detecting the signature of primordial non-Gaussianity produced during or right after an inflationary period is more challenging but still possible. An ideal experiment limited by cosmic variance only and with an angular resolution of a few arcseconds has the potential to detect primordial non-Gaussianity with a nonlinearity parameter of fNL~1. Additional sources of error such as weak lensing and an imperfect foreground subtraction could severely hamper the detection of primordial non-Gaussianity, which will benefit from the use of optimal estimators combined with tomographic techniques.