PREPRINT
C0B101BE-C7DA-4802-8511-53061048FE40

# Squeezing ${\mathbit{f}}_{\mathrm{N}\mathrm{L}}$ out of the matter bispectrum with consistency relations

Samuel Goldstein, Angelo Esposito, Oliver H. E. Philcox, Lam Hui, J. Colin Hill, Roman Scoccimarro, Maximilian H. Abitbol

Submitted on 13 September 2022

## Abstract

We show how consistency relations can be used to robustly extract the amplitude of local primordial non-Gaussianity (${f}_{\mathrm{N}\mathrm{L}}$) from the squeezed limit of the matter bispectrum, well into the non-linear regime. First, we derive a non-perturbative relation between primordial non-Gaussianity and the leading term in the squeezed bispectrum, revising some results present in the literature. This relation is then used to successfully measure ${f}_{\mathrm{N}\mathrm{L}}$ from $N$-body simulations. We discuss the dependence of our results on different scale cuts and redshifts. Specifically, the analysis is strongly dependent on the choice of the smallest soft momentum, ${q}_{\mathrm{m}\mathrm{i}\mathrm{n}}$, which is the most sensitive to primordial bispectrum contributions, but is largely independent of the choice of the largest hard momentum, ${k}_{\mathrm{m}\mathrm{a}\mathrm{x}}$, due to the non-Gaussian nature of the covariance. We also show how the constraints on ${f}_{\mathrm{N}\mathrm{L}}$ improve at higher redshift, due to a reduced off-diagonal covariance. In particular, for a simulation with ${f}_{\mathrm{N}\mathrm{L}}=100$ and a volume of , we measure ${f}_{\mathrm{N}\mathrm{L}}=98±12$ at redshift $z=0$ and ${f}_{\mathrm{N}\mathrm{L}}=97±8$ at $z=0.97$. Finally, we compare our results with a Fisher forecast, showing that the current version of the analysis is satisfactorily close to the Fisher error. We regard this as a first step towards the realistic application of consistency relations to constrain primordial non-Gaussianity using observations.

## Preprint

Comment: 16 pages, 8 figures

Subjects: Astrophysics - Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology; High Energy Physics - Theory