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, $q_{\min }$, 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 $f_{\mathrm{NL}}$ 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 $(2.4\mathrm{Gpc}/h{)}^3$, we measure $f_{\mathrm{NL}}=98\pm 12$ at redshift $z=0$ and $f_{\mathrm{NL}}=97\pm 8$ 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.

• Received 16 September 2022
• Accepted 2 December 2022

DOI:https://doi.org/10.1103/PhysRevD.106.123525

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society