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

Zackary Brown, R. Demina+48 more|DIGITAL.CSIC (Spanish National Research Council (CSIC))|Mar 27, 2024

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes a novel method to constrain primordial non-Gaussianity (fNL) using the configuration-space two-point and three-point correlation functions (2pcf and 3pcf) of large-scale structure tracers, such as luminous red galaxies (LRGs) from the DESI survey. By modeling the scale-dependent bias induced by local fNL on simulated dark matter halos and scaling it to observed tracers, the authors demonstrate a precision of σfNL ≈ 22 with one year of DESI data, offering a competitive alternative to Fourier-space power spectrum and bi-spectrum analyses.

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.

Motivation & Objective

• To develop a robust framework for measuring local primordial non-Gaussianity (PNG) using configuration-space correlation functions instead of Fourier-space power spectra and bi-spectra.
• To model the scale-dependent bias induced by fNL on large-scale structure clustering, particularly in the context of luminous red galaxies (LRGs).
• To demonstrate the feasibility and precision of this method using FastPM-L3 halo simulations and forecast constraints for the DESI survey.
• To enable application of this method to other cosmological tracers and future surveys like Euclid by calibrating the model on fiducial simulations and accounting for observational systematics.
• To improve sensitivity to PNG by combining 2pcf and 3pcf monopoles, enhancing constraints beyond single-statistic approaches.

Proposed method

• The method models the scale-dependent bias from local PNG on dark matter halo clustering using FastPM-L3 simulations, capturing the effect of fNL on the 2pcf and 3pcf monopoles.
• The framework scales the simulated halo clustering response to an arbitrary matter tracer (e.g., LRGs) using a parameter p that controls the amplitude of the bias response.
• The 2pcf and 3pcf monopoles are measured from the simulated tracer catalogues to estimate the fNL signal, with the covariance matrix derived from ensemble simulations.
• The method is validated using both toy-model data and high-fidelity EZ mocks, confirming robustness and consistency in fNL estimation.
• Observational systematics such as imaging, completeness, redshift failures, and fiber assignment are modeled via nuisance parameters and weights, to be marginalized in the final likelihood.
• The approach is generalizable to any tracer with available fiducial simulations and a known bias response, enabling application to DESI and future surveys like Euclid.

Experimental results

Research questions

• RQ1 Can the configuration-space 2pcf and 3pcf monopoles jointly constrain fNL more effectively than traditional Fourier-space methods?
• RQ2 How does local primordial non-Gaussianity induce scale-dependent bias in the clustering of large-scale structure tracers like LRGs?
• RQ3 What is the expected precision on fNL using one year of DESI survey data when combining 2pcf and 3pcf signals?
• RQ4 How can observational systematics such as survey completeness and redshift failures be effectively modeled and marginalized in fNL estimation?
• RQ5 To what extent can the bias response from dark matter halos be scaled to real galaxy tracers like LRGs using a single parameter p?

Key findings

• The method achieves a forecasted precision of σfNL ≈ 22 for local primordial non-Gaussianity using one year of DESI survey data, demonstrating strong constraining power.
• The framework successfully captures the scale-dependent bias from fNL on both 2pcf and 3pcf monopoles, with consistent results across multiple simulation sets including EZ mocks and FastPM-L3 simulations.
• The inclusion of both 2pcf and 3pcf monopoles enhances sensitivity to fNL compared to using either statistic alone, confirming the benefit of multi-point correlation function analysis.
• The model remains robust when accounting for key observational systematics, provided they are modeled as nuisance parameters with appropriate weights.
• The method is generalizable: with fiducial simulations and a bias response parameter p, it can be applied to any cosmological tracer, including future DESI tracers and Euclid data.
• The results confirm that configuration-space correlation functions offer a viable and competitive alternative to Fourier-space bi-spectrum methods for PNG constraints.