Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity

TL;DR

We develop an efficient method to generate non-local PNG initial conditions for N-body simulations using a quadratic kernel that yields equilateral and orthogonal templates through separable generators, enabling FFT-based computation with modest overhead. We derive a general peak-background split (PBS) formula for the scale-dependent halo bias in non-local PNG, extending beyond local bias to include non-Markovian and non-universal mass-function effects, and we obtain the leading quadratic bias results for arbitrary non-local PNG. The approach is validated against LasDamas simulations for local, equilateral, and orthogonal PNG, showing improved agreement with measured halo bias and confirming that nonlinear bias loop corrections are small on large scales. These results enable robust constraints on non-local PNG from measurements of the power spectrum and bispectrum in galaxy surveys, providing a practical route to exploiting non-local PNG in large-scale structure analyses.

Abstract

We study the scale-dependence of halo bias in generic (non-local) primordial non-Gaussian (PNG) initial conditions of the type motivated by inflation, parametrized by an arbitrary quadratic kernel. We first show how to generate non-local PNG initial conditions with minimal overhead compared to local PNG models for a general class of primordial bispectra that can be written as linear combinations of separable templates. We run cosmological simulations for the local, and non-local equilateral and orthogonal models and present results on the scale-dependence of halo bias. We also derive a general formula for the Fourier-space bias using the peak-background split (PBS) in the context of the excursion set approach to halos and discuss the difference and similarities with the known corresponding result from local bias models. Our PBS bias formula generalizes previous results in the literature to include non-Markovian effects and non-universality of the mass function and are in better agreement with measurements in numerical simulations than previous results for a variety of halo masses, redshifts and halo definitions. We also derive for the first time quadratic bias results for arbitrary non-local PNG, and show that non-linear bias loops give small corrections at large-scales. The resulting well-behaved perturbation theory paves the way to constrain non-local PNG from measurements of the power spectrum and bispectrum in galaxy redshift surveys.