Halo Clustering with Non-Local Non-Gaussianity

TL;DR

This paper extends the peak-background split method to predict halo clustering effects caused by various types of primordial non-Gaussianity, revealing scale-dependent biases and their potential observational constraints.

Contribution

It generalizes the peak-background split to arbitrary bispectra and compares its predictions with local biasing, highlighting differences and implications for non-Gaussian models.

Findings

Peak-background split agrees with local biasing on large scales for local non-Gaussianity.

Predictions diverge on smaller scales due to scale separation assumptions.

Non-local models show weaker scale dependence of bias, but still potentially constrainable.

Abstract

We show how the peak-background split can be generalized to predict the effect of non-local primordial non-Gaussianity on the clustering of halos. Our approach is applicable to arbitrary primordial bispectra. We show that the scale-dependence of halo clustering predicted in the peak-background split (PBS) agrees with that of the local-biasing model on large scales. On smaller scales, k >~ 0.01 h/Mpc, the predictions diverge, a consequence of the assumption of separation of scales in the peak-background split. Even on large scales, PBS and local biasing do not generally agree on the amplitude of the effect outside of the high-peak limit. The scale dependence of the biasing - the effect that provides strong constraints to the local-model bispectrum - is far weaker for the equilateral and self-ordering-scalar-field models of non-Gaussianity. The bias scale dependence for the orthogonal and folded models is weaker than in the local model (~ 1/k), but likely still strong enough to be constraining. We show that departures from scale-invariance of the primordial power spectrum may lead to order-unity corrections, relative to predictions made assuming scale-invariance - to the non-Gaussian bias in some of these non-local models for non-Gaussianity. An Appendix shows that a non-local model can produce the local-model bispectrum, a mathematical curiosity we uncovered in the course of this investigation.