Primordial non-Gaussianity in the Bispectrum of the Halo Density Field

TL;DR

This paper derives the halo bispectrum at tree level to probe primordial non-Gaussianity, showing that it can provide tighter constraints on early Universe processes than the power spectrum.

Contribution

It presents a new tree level derivation of the halo bispectrum including non-Gaussian effects and develops a diagrammatic approach for understanding its scale and shape dependence.

Findings

Non-Gaussian modifications amplify the bispectrum.

Results agree with simulation measurements.

Bispectrum analysis can constrain fNL more effectively than power spectrum.

Abstract

The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. Finally, we estimate the expected signal to noise on fNL and show that the constraint obtainable from the bispectrum analysis significantly exceeds the one obtainable from the power spectrum analysis.