The trispectrum of 21-cm background anisotropies as a probe of primordial non-Gaussianity

The 21-cm anisotropies from the neutral hydrogen distribution prior to the era of reionization is a sensitive probe of primordial non-Gaussianity. Unlike the case with cosmic microwave background, 21-cm anisotropies provide multi-redshift information with frequency selection and is not damped at arcminute angular scales. We discuss the angular trispectrum of the 21-cm background anisotropies and discuss how the trispectrum signal generated by the primordial non-Gaussianity can be measured with the three-to-one correlator and the corresponding angular power spectrum. We also discuss the separation of primordial non-Gaussian information in the trispectrum with that generated by the subsequent non-linear gravitational evolution of the density field. While with the angular bispectrum of 21-cm anisotropies one can limit the second order corrections to the primordial fluctuations below f_NL< 1, using the trispectrum information we suggest that the third order coupling term, f_2 or g_NL, can be constrained to be arounde 10 with future 21-cm observations over the redshift interval of 50 to 100.