Beyond the two-point correlation: constraining primordial non-gaussianity with density perturbation moments

Constraining primordial non-Gaussianities (PNGs) in the large-scale cosmic structure (LSS) is an important step in understanding properties of the early universe, specifically in distinguishing between different inflationary models. Measuring PNG relies on evaluating the scale-dependent correlations in the density field. New summary statistics beyond the two- and three-point correlation functions in configuration space and their Fourier-space counterparts, the power- and bi-spectrum may provide increased sensitivity. We introduce a new method for extracting the PNG signal imprinted on the LSS by using the first three Gaussian moments of the normalized correlation in density perturbations, evaluated at varying distance scales. We aim to assess this method's sensitivity to local PNG, parameterized by $f_ {\mathrm{NL}}$. We perform spherical convolutions at a range of scales on dark matter halo simulations to measure the scale-dependent correlations in the density field. From these, we compute the first three moments and compare them to a model expectation vector, parameterized to the second power in $f_{\mathrm{NL}}$. Our method provides about 21% improvement in sensitivity to $f_{\mathrm{NL}}$ with respect to using the two point correlation function alone. Notably, we find that the second moment alone carries nearly as much constraining power as the mean, highlighting the potential of higher-order statistics. Given its simplicity and efficiency, this framework is well-suited for application to current and upcoming large-scale surveys such as DESI.