An Effective Theory for Biased Tracers via the Boltzmann-Equation Approach

TL;DR

This paper introduces an effective theory for biased tracers using the Boltzmann equation, unifying density and velocity bias modeling with a collision term approach, and accurately predicting large-scale structure power spectra.

Contribution

It develops a novel Boltzmann-equation-based framework for biased tracers, incorporating a general collision term to unify density and velocity bias descriptions.

Findings

Predicts time- and scale-dependent bias parameters.

Reproduces power spectrum up to k^4 with fewer parameters.

Clarifies the origin of velocity bias and higher-derivative effects.

Abstract

We develop an effective theory for biased tracers formulated at the level of the Boltzmann equation, providing a unified description of density and velocity bias. We introduce a general effective collision term in the tracer Boltzmann equation to encode tracer dynamics that are intrinsically different from those of dark matter. This collision operator leads to modified continuity and Euler equations, with source terms reflecting the collision-term physics. At linear order, this framework predicts time- and scale-dependent bias parameters in a self-consistent manner, encompassing peak bias as a special case while clarifying how velocity bias and higher-derivative effects arise. Applying the resulting bias model to redshift-space distortions, we show that the Boltzmann-equation approach reproduces the power spectrum of biased tracers obtained in the Effective Field Theory of Large-Scale Structure up to $k^4$ terms with fewer independent parameters.