  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.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory