Quijote-PNG: Quasi-maximum Likelihood Estimation of Primordial Non-Gaussianity in the Nonlinear Halo Density Field

We study primordial non-Gaussian signatures in the redshift-space halo field on nonlinear scales, using a quasi-maximum likelihood estimator based on optimally compressed power spectrum and modal bispectrum statistics. We train and validate the estimator on a suite of halo catalogs constructed from the Quijote-png N -body simulations, which we release to accompany this paper. We verify its unbiasedness and near-optimality for the three main types of primordial non-Gaussianity (PNG): local, equilateral, and orthogonal. We compare the modal bispectrum expansion with a k -binning approach, showing that the former allows for faster convergence of numerical derivatives in the computation of the score function, thus leading to better final constraints. We find, in agreement with previous studies, that the local PNG signal in the halo field is dominated by the scale-dependent bias signature on large scales and saturates at k ∼ 0.2 h Mpc ^−1 , whereas the small-scale bispectrum is the main source of information for equilateral and orthogonal PNG. Combining the power spectrum and bispectrum on nonlinear scales plays an important role in breaking degeneracies between cosmological and PNG parameters; such degeneracies, however, remain strong for equilateral PNG. We forecast that PNG parameters can be constrained with ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{local}}=45$ , ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{equil}}=570$ , and ${\rm{\Delta }}{f}_{\mathrm{NL}}^{\mathrm{ortho}}=110$ on a cubic volume of $1{\left(\mathrm{Gpc}\,{h}^{-1}\right)}^{3}$ at z = 1, considering scales up to ${k}_{\max }=0.5\,h\,{\mathrm{Mpc}}^{-1}$ .