Squeezing $f_{\rm NL}$ out of the matter bispectrum with consistency relations

TL;DR

This paper demonstrates how consistency relations can be used to accurately measure primordial non-Gaussianity parameter $f_{NL}$ from the matter bispectrum in the non-linear regime, validated through simulations and analysis of redshift dependence.

Contribution

It derives a non-perturbative relation linking primordial non-Gaussianity to the squeezed bispectrum and applies it to measure $f_{NL}$ from simulations, improving understanding of its observational constraints.

Findings

Successful measurement of $f_{NL}$ from simulations at different redshifts.

Measurement precision improves at higher redshift due to covariance reduction.

The method aligns well with Fisher forecast predictions.

Abstract

We show how consistency relations can be used to robustly extract the amplitude of local primordial non-Gaussianity ($f_{\rm NL}$) 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 $f_{\rm NL}$ 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, $q_{\rm min}$, which is the most sensitive to primordial bispectrum contributions, but is largely independent of the choice of the largest hard momentum, $k_{\rm max}$, due to the non-Gaussian nature of the covariance. We also show how the constraints on $f_{\rm NL}$ improve at higher redshift, due to a reduced off-diagonal covariance. In particular, for a simulation with $f_{\rm NL} = 100$ and a volume of $(2.4 \text{ Gpc}/h)^3$, we measure $f_{\rm NL} = 98 \pm 12$ at redshift $z=0$ and $f_{\rm NL} = 97 \pm 8$ 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.