Squeezing fNL out of the matter bispectrum with consistency relations

We show how consistency relations can be used to robustly extract the amplitude of local primordial non-Gaussianity (fNL) 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 fNL 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_min, which is the most sensitive to primordial bispectrum contributions, but is largely independent of the choice of the largest hard momentum, k_max, due to the non-Gaussian nature of the covariance. We also show how the constraints on fNL improve at higher redshift, due to a reduced off-diagonal covariance. In particular, for a simulation with fNL = 100 and a volume of (2.4 Gpc / h)^3, we measure fNL = 98 ± 12 at redshift z = 0 and fNL = 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.