Biased Tracers and Time Evolution

TL;DR

This paper investigates how galaxy bias evolves over time, proposing a finite set of operators to describe galaxy density contrast at any perturbation order, with implications for effective theory and renormalization.

Contribution

It introduces a systematic basis of operators for galaxy bias evolution, extending previous expansions and applicable at all perturbation orders, with a detailed third order validation.

Findings

Basis spans a larger space than traditional expansions.

New operators appear only at fourth order.

Basis is closed under renormalization.

Abstract

We study the effect of time evolution on galaxy bias. We argue that at any order in perturbations, the galaxy density contrast can be expressed in terms of a finite set of locally measurable operators made of spatial and temporal derivatives of the Newtonian potential. This is checked in an explicit third order calculation. There is a systematic way to derive a basis for these operators. This basis spans a larger space than the expansion in gravitational and velocity potentials usually employed, although new operators only appear at fourth order. The basis is argued to be closed under renormalization. Most of the arguments also apply to the structure of the counter-terms in the effective theory of large-scale structure.