Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions

TL;DR

The paper develops a framework to constrain local primordial non-Gaussianity via configuration-space two-point and three-point correlation functions (2pcf and 3pcf) monopoles, using ConKer to efficiently compute these statistics and a linearized PNG bias model to interpolate for arbitrary $f_{ m NL}$. It validates the method on simulated DESI LRG catalogs (SY5, Y1) and independent FastPM/AbacusSummit mocks, showing that the 2pcf carries most sensitivity while the 3pcf adds complementary information, and demonstrates forecasted constraints of $\sigma_{f_{ m NL}} \approx 22$ for DESI Year-1. The approach includes a robust statistical pipeline with fiducial simulations, cross-validation against non-PNG realizations, and careful treatment of nuisance parameters and systematics, highlighting its potential for cross-checks with Fourier-space analyses. Overall, the framework offers a scalable, tomography-ready route to leveraging large-volume LSS data to probe inflationary physics through local PNG signals, with applicability to DESI, Euclid, and other upcoming surveys.

Abstract

Surveys of cosmological large-scale structure (LSS) are sensitive to the presence of local primordial non-Gaussianity (PNG), and may be used to constrain models of inflation. Local PNG, characterized by fNL, the amplitude of the quadratic correction to the potential of a Gaussian random field, is traditionally measured from LSS two-point and three-point clustering via the power spectrum and bi-spectrum. We propose a framework to measure fNL using the configuration space two-point correlation function (2pcf) monopole and three-point correlation function (3pcf) monopole of survey tracers. Our model estimates the effect of the scale-dependent bias induced by the presence of PNG on the 2pcf and 3pcf from the clustering of simulated dark matter halos. We describe how this effect may be scaled to an arbitrary tracer of the cosmological matter density. The 2pcf and 3pcf of this tracer are measured to constrain the value of fNL. Using simulations of luminous red galaxies observed by the Dark Energy Spectroscopic Instrument (DESI), we demonstrate the accuracy and constraining power of our model, and forecast the ability to constrainfNL to a precision of sigma(fNL) = 22 with one year of DESI survey data.

Figures (16)

• Figure 1: An illustration of the two ($0-1$) and three ($0-1-2$) point correlation function evaluation using ConKer. The blue spherical kernels of radii $s$ for the 2pcf and $s_1$ and $s_2$ for the 3pcf are convolved with the matter distributions. The integration over $\vec{r}$ is performed by scanning the position of the kernel center $0$ over the surveyed volume.
• Figure 2: The angular coverage (top left) and the redshift distribution (bottom right) of the DESI SY5 (grey) and Y1 (cyan) LRG simulations.
• Figure 3: Top: The average diagonal $n$pcfs $\xi_n^{\mathrm{di}}$ when $n=2,3$ for the SY5 EZ mocks (grey) and AbacusSummit simulation (green), as a function of the distance scale, $s$. The shaded region shows uncertainties estimated from the covariance matrix for the SY5 EZ mocks (grey) and Y1 EZ mocks (cyan). The thin green lines show the $n$pcfs for each realization of the AbacusSummit simulations independently. The diagonal $n$pcfs are multiplied by $\tilde{s}^n$, where $\tilde{s} = (s/100\ h^{-1}\mathrm{Mpc})$, to emphasize features at large scales. Bottom: The 3pcf $\xi_3$ for the SY5 EZ mocks (grey) and AbacusSummit simulation (green), as a function of the triangle index where $s_1 > s_2$. The 3pcf is multiplied by $\tilde{s}_1^2 \tilde{s}_2^2$. In all panels, the dashed black horizontal line denotes 0.
• Figure 4: The correlation matrix $C_{ij} = C_{ij}/ \sqrt{C_{ii} C_{jj}}$, derived from the ensemble of SY5 EZ mocks.
• Figure 5: The $n$pcfs $\xi_n^{\mathrm{di}}$ for $n=2,3$ (upper panels) for the ensemble of the FastPM-L3 simulated halos with $f_{\mathrm{NL}} = 0$ (blue), $100$ (red), and the estimate of $A_n$ (lower panels). The shaded regions show uncertainties estimated from the covariance matrix of each ensemble. Top: The diagonal $n$pcfs and $A_n$ multiplied by $\tilde{s}^n$ are shown as functions of the distance scale, $s$. Bottom: 3pcf and $A_3$ multiplied by $\tilde{s}_1^2 \tilde{s}_2^2$ are shown as a function of the triangle index. In all panels, the dashed black horizontal line denotes 0.