Halo Clustering with Non-Local Non-Gaussianity

TL;DR

This work generalizes the peak-background split to arbitrary non-local quadratic primordial non-Gaussianity, deriving the non-Gaussian halo bias for general bispectra and applying the results to equilateral, folded, orthogonal, SOSF, and local shapes. It demonstrates that PBS reproduces the large-scale scale-dependence of halo bias predicted by local biasing, but diverges on smaller scales due to the breakdown of scale separation, with amplitude differences outside the high-peak regime. The analysis shows that equilateral and SOSF models yield much weaker bias scale-dependence, while folded and orthogonal models can produce stronger, potentially constraining signals, and that deviations from scale-invariance can induce order-unity corrections for some non-local shapes. An Appendix reveals that a non-local inflationary model can generate the local-model bispectrum, highlighting the non-uniqueness of kernel realizations and the subtlety of mapping from primordial to processed spectra. Overall, the paper provides a structured framework to test non-local non-Gaussianity with halo clustering, pending validation by N-body simulations.

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.

Figures (4)

• Figure 1: Squeezed limit of $\widetilde{W}(q,\mu)$ as function of $q$ for equilateral (top) and folded (bottom) bispectra. Here, we have taken out the leading $q$ scaling and adopted a fixed value of $\mu=0.5$. Shown is the exact result from Eq. (\ref{['eq:Wtilde']}), and the series expansion of the squeezed limit to $\mathcal{O}(q^2,\varepsilon^2)$ from § \ref{['sec:squeezed']}. We also show the scale-free limit of this series expansion, which in general is not a good approximation.
• Figure 2: Non-Gaussian correction to the halo bias $\Delta b_L$ calculated in the peak-background-split (PBS) and local-bias approaches as a function of $k$, for the equilateral (top) and SOSF (bottom) bispectra. We have assumed $f_{\rm NL}=100$ in both cases and $M=10^{13}\,M_{\odot}/h$ halos at $z=0$. We also show the scale-free approximations Eqs. (\ref{['eq:Dbsf-eql']})--(\ref{['eq:Dbsf-fol']}).
• Figure 3: Same as Fig. \ref{['fig:Deltab']}, but for the folded (top) and orthogonal (bottom) models. We have taken out a scaling factor of $(k/0.01\,h~{\rm Mpc}^{-1})^{-1}$.
• Figure 4: Same as Fig. \ref{['fig:Deltab']}, but now for the local model. We have taken out a scaling of $(k/0.01\,h~{\rm Mpc}^{-1})^{-2}$ here.