Squeezing fNL out of the matter bispectrum with consistency relations

Abstract

We show how consistency relations can be used to robustly extract the amplitude of local primordial non-Gaussianity (${f}_{\mathrm{NL}}$) from the squeezed limit of the matter bispectrum, well into the nonlinear regime. First, we derive a nonperturbative 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 ${f}_{\mathrm{NL}}$ 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, ${q}_{\mathrm{min}}$, which is the most sensitive to primordial bispectrum contributions, but is largely independent of the choice of the largest hard momentum, ${k}_{\mathrm{max}}$, due to the non-Gaussian nature of the covariance. We also show how the constraints on ${f}_{\mathrm{NL}}$ improve at higher redshift, due to a reduced off-diagonal covariance. In particular, for a simulation with ${f}_{\mathrm{NL}}=100$ and a volume of $(2.4\text{ }\text{ }\mathrm{Gpc}/h{)}^{3}$, we measure ${f}_{\mathrm{NL}}=98\ifmmode\pm\else\textpm\fi{}12$ at redshift $z=0$ and ${f}_{\mathrm{NL}}=97\ifmmode\pm\else\textpm\fi{}8$ 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.