Halo clustering with nonlocal non-Gaussianity

We show how the peak-background split (PBS) can be generalized to predict the effect of nonlocal 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 agrees with that of the local-biasing model on large scales. On smaller scales, k≳0.01hMpc^-1, 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 (∼k^-1), 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 nonlocal models for non-Gaussianity. An Appendix shows that a nonlocal model can produce the local-model bispectrum, a mathematical curiosity we uncovered in the course of this investigation.