Scale Dependence of the Halo Bias in General Local-Type Non-Gaussian Models I: Analytical Predictions and Consistency Relations

TL;DR

This paper derives analytical predictions for how primordial non-Gaussianities affect halo clustering and bias in cosmology, introducing new inequalities and methods to distinguish different non-Gaussian models.

Contribution

It provides a general formula for halo power spectrum with non-Gaussianities, introduces a new inequality for multi-field non-Gaussianity testing, and discusses how to differentiate non-Gaussian types using bias measurements.

Findings

Derived a general halo power spectrum formula incorporating non-Gaussianities.

Introduced a new inequality extending the Suyama-Yamaguchi relation for multi-field models.

Showed that bias amplitude can distinguish between quadratic and higher-order non-Gaussianities.

Abstract

We investigate the clustering of halos in cosmological models starting with general local-type non-Gaussian primordial fluctuations. We employ multiple Gaussian fields and add local-type non-Gaussian corrections at arbitrary order to cover a class of models described by frequently-discussed f_nl, g_nl and \tau_nl parameterization. We derive a general formula for the halo power spectrum based on the peak-background split formalism. The resultant spectrum is characterized by only two parameters responsible for the scale-dependent bias at large scale arising from the primordial non-Gaussianities in addition to the Gaussian bias factor. We introduce a new inequality for testing non-Gaussianities originating from multi fields, which is directly accessible from the observed power spectrum. We show that this inequality is a generalization of the Suyama-Yamaguchi inequality between f_nl and \tau_nl to the primordial non-Gaussianities at arbitrary order. We also show that the amplitude of the scale-dependent bias is useful to distinguish the simplest quadratic non-Gaussianities (i.e., f_nl-type) from higher-order ones (g_nl and higher), if one measures it from multiple species of galaxies or clusters of galaxies. We discuss the validity and limitations of our analytic results by comparison with numerical simulations in an accompanying paper.