PREPRINT
2762B43D-C3E5-4917-8691-E2F9556B0F98

# Primordial non-Gaussianity with Angular correlation function: Integral constraint and validation for DES

Walter Riquelme, Santiago Avila, Juan Garcia-Bellido, Anna Porredon, Ismael Ferrero, Kwan Chuen Chan, Rogerio Rosenfeld, Hugo Camacho, Adrian G. Adame, Aurelio Carnero Rosell, Martin Crocce, Juan De Vicente, Tim Eifler, Jack Elvin-Poole, Xiao Fang, Elisabeth Krause, Martin Rodriguez Monroy, Ashley J. Ross, Eusebio Sanchez, Ignacio Sevilla

Submitted on 15 September 2022

## Abstract

Local primordial non-Gaussianity (PNG) is a promising observable of the underlying physics of inflation, characterized by a parameter denoted by ${f}_{\mathrm{N}\mathrm{L}}$. We present the methodology to measure local ${f}_{\mathrm{N}\mathrm{L}}$ from the Dark Energy Survey (DES) data using the 2-point angular correlation function (ACF) via the induced scale-dependent bias. One of the main focuses of the work is the treatment of the integral constraint. This condition appears when estimating the mean number density of galaxies from the data and is especially relevant for PNG analyses, where it is found to be key in obtaining unbiased ${f}_{\mathrm{N}\mathrm{L}}$ constraints. The methods are analysed for two types of simulations: $\sim 246$ GOLIAT N-body simulations with non-Gaussian initial conditions ${f}_{\mathrm{N}\mathrm{L}}$ equal to -100 and 100, and 1952 Gaussian ICE-COLA mocks with ${f}_{\mathrm{N}\mathrm{L}}=0$ that follow the DES angular and redshift distribution. We use the GOLIAT mocks to asses the impact of the integral constraint when measuring ${f}_{\mathrm{N}\mathrm{L}}$. We obtain biased PNG constraints when ignoring the integral constraint, ${f}_{\mathrm{N}\mathrm{L}}=-2.8±1.0$ for ${f}_{\mathrm{N}\mathrm{L}}=100$ simulations, and ${f}_{\mathrm{N}\mathrm{L}}=-10.3±1.5$ for ${f}_{\mathrm{N}\mathrm{L}}=-100$ simulations, whereas we recover the fiducial values within $1\sigma$ when correcting for the integral constraint with ${f}_{\mathrm{N}\mathrm{L}}=97.4±3.5$ and ${f}_{\mathrm{N}\mathrm{L}}=-95.2±5.4$, respectively. We use the ICE-COLA mocks to validate our analysis in a DES-like setup, finding it to be robust to different analysis choices: best-fit estimator, the effect of integral constraint, the effect of BAO damping, the choice of covariance, and scale configuration. We forecast a measurement of ${f}_{\mathrm{N}\mathrm{L}}$ within $\sigma \left({f}_{\mathrm{N}\mathrm{L}}\right)=31$ when using the DES-Y3 BAO sample, with the ACF in the range.

## Preprint

Comment: 16 pages, 10 figures

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics