Primordial non-Gaussianity and non-Gaussian covariance

In the pursuit of primordial non-Gaussianities, we hope to access smaller scales across larger comoving volumes. At low redshift, the search for primordial non-Gaussianities is hindered by gravitational collapse, with which we often associate a scale k L. Beyond these scales, it will be hard to reconstruct the modes sensitive to the primordial distribution. When forecasting future constraints on the amplitude of primordial non-Gaussianity, f L, off-diagonal components are usually neglected in the covariance because they are small compared to the diagonal components. We show that the induced non-Gaussian off-diagonal components in the covariance degrade forecast constraints on primordial non-Gaussianity, even when all modes are well within what is usually considered the linear regime. As a testing ground, we examine the effects of these off-diagonal components on the constraining power of the matter bispectrum on fL as a function of kmax and redshift, confirming our results against N -body simulations out to redshift z 1/4 10. We then consider these effects on the hydrogen bispectrum as observed from a PUMA-like 21-cm intensity mapping survey at redshifts 2 < z < 6 and show that not including off-diagonal covariance overpredicts the constraining power on fL by up to a factor of 5. For future surveys targeting even higher redshifts, such as Cosmic Dawn and the Dark Ages, which are considered ultimate surveys for primordial non-Gaussianity, we predict that non-Gaussian covariance would severely limit prospects to constrain fL from the bispectrum.