Probing the bispectrum at high redshifts using 21‐cm H i observations

Observations of fluctuations in the redshifted 21‐cm radiation from neutral hydrogen (H  i ) are perceived to be an important future probe of the universe at high redshifts. Under the assumption that at redshifts z ≤ 6 (post‐reionization era) the H  i traces the underlying dark matter with a possible bias, we investigate the possibility of using observations of redshifted 21‐cm radiation to detect the bispectrum arising from non‐linear gravitational clustering and from non‐linear bias. We find that the expected signal is ∼ 0.1  mJy at 325  MHz ( z = 3.4) for the small baselines at the Giant Metrewave Radio Telescope, the strength being a few times larger at higher frequencies (610 MHz, z = 1.3) . Further, the magnitude of the signal from the bispectrum is predicted to be comparable to that from the power spectrum, allowing a detection of both in roughly the same integration time. The H  i signal is found to be uncorrelated beyond frequency separations of ∼1.3 MHz whereas the continuum sources of contamination are expected to be correlated across much larger frequencies. This signature can in principle be used to distinguish the H  i signal from the contamination. We also consider the possibility of using observations of the bispectrum to determine the linear and quadratic bias parameters of the H  i at high redshifts, this having possible implications for theories of galaxy formation.