Beyond the two-point correlation: Constraining primordial non-Gaussianity with density-perturbation moments

¹ Department of Physics and Astronomy, University of Rochester, 500 Joseph C. Wilson Boulevard, Rochester, NY 14627, USA
² Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
³ Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506, USA
⁴ Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

^★ Corresponding author: ethanvis322@gmail.com

Received: 20 August 2025
Accepted: 25 October 2025

Abstract

Context. Constraining primordial non-Gaussianity (PNG) on 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 bispectrum may provide increased sensitivity.

Aims. 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 on varying distance scales. We aim to assess this method’s sensitivity to local PNG, parameterized by f_NL.

Methods. We performed spherical convolutions on a range of scales on dark-matter-halo simulations to measure the scale-dependent correlations in the density field. From these, we computed the first three moments and compared them to a model expectation vector, parameterized to the second power in f_NL.

Results. Our method provides about 21% improvement in sensitivity to f_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 the Dark Energy Spectroscopic Instrument (DESI).