Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS

TL;DR

This paper extends the perturbative bias model for large-scale structure by including additional dependencies on gravitational and velocity fields, introducing only two new parameters to accurately model clustering up to 4th order.

Contribution

The authors generalize the bias model to incorporate local gravitational and velocity effects with minimal additional parameters, improving modeling of galaxy clustering.

Findings

Only two new free parameters needed for 4th order modeling.

Inclusion of non-locality through higher derivative terms.

Enhanced potential for extracting information from future large surveys.

Abstract

On very large scales, density fluctuations in the Universe are small, suggesting a perturbative model for large-scale clustering of galaxies (or other dark matter tracers), in which the galaxy density is written as a Taylor series in the local mass density, delta, with the unknown coefficients in the series treated as free "bias" parameters. We extend this model to include dependence of the galaxy density on the local values of nabla_i nabla_j phi and nabla_i v_j, where phi is the potential and v is the peculiar velocity. We show that only two new free parameters are needed to model the power spectrum and bispectrum up to 4th order in the initial density perturbations, once symmetry considerations and equivalences between possible terms are accounted for. One of the new parameters is a bias multiplying s_ij s_ji, where s_ij=[nabla_i nabla_j \nabla^-2 - 1/3 delta^K_ij] delta. The other multiplies s_ij t_ji, where t_ij=[nabla_i nabla_j nabla^-2 - 1/3 delta^K_ij](theta-delta), with theta=-(a H dlnD/dlna)^-1 nabla_i v_i. (There are other, observationally equivalent, ways to write the two terms, e.g., using theta-delta instead of s_ij s_ji.) We show how short-range (non-gravitational) non-locality can be included through a controlled series of higher derivative terms, starting with R^2 nabla^2 delta, where R is the scale of non-locality (this term will be a small correction as long as k^2 R^2 is small, where k is the observed wavenumber). We suggest that there will be much more information in future huge redshift surveys in the range of scales where beyond-linear perturbation theory is both necessary and sufficient than in the fully linear regime.