Cubic Halo Bias in Eulerian and Lagrangian Space

TL;DR

This paper develops a new method to estimate cubic bias parameters in halo clustering using cross-spectra, revealing significant local and non-local cubic biases and challenging some local Lagrangian bias predictions.

Contribution

It extends the quadratic field method to cubic fields for bias estimation, enabling detection of cubic bias parameters and their comparison with theoretical models.

Findings

Significant detection of local and non-local cubic bias parameters.

Partial tension with local Lagrangian bias predictions.

Detection of non-local quadratic bias in Lagrangian space.

Abstract

Predictions of the next-to-leading order, i.e. one-loop, halo power spectra depend on local and non-local bias parameters up to cubic order. The linear bias parameter can be estimated from the large scale limit of the halo-matter power spectrum, and the second order bias parameters from the large scale, tree-level, bispectrum. Cubic operators would naturally be quantified using the tree-level trispectrum. As the latter is computationally expensive, we extent the quadratic field method proposed in Schmittfull et al. 2014 to cubic fields in order to estimate cubic bias parameters. We cross-correlate a basis set of cubic bias operators with the halo field and express the result in terms of the cross-spectra of these operators in order to cancel cosmic variance. We obtain significant detections of local and non-local cubic bias parameters, which are partially in tension with predictions based on local Lagrangian bias schemes. We directly measure the Lagrangian bias parameters of the protohaloes associated with our halo sample and clearly detect a non-local quadratic term in Lagrangian space. We do not find a clear detection of non-local cubic Lagrangian terms for low mass bins, but there is some mild evidence for their presence for the highest mass bin. While the method presented here focuses on cubic bias parameters, the approach could also be applied to quantifications of cubic primordial non-Gaussianity.