Galaxy bias renormalization group

TL;DR

This paper develops a systematic renormalization group approach for galaxy bias in large-scale structure, enabling more consistent and robust extraction of cosmological information from galaxy clustering data.

Contribution

It introduces a finite-cutoff renormalization scheme for galaxy bias parameters, connecting it with standard $n$-point function renormalization and addressing current inconsistencies.

Findings

Derived Wilson-Polchinski RG equations for bias parameters

Connected finite-cutoff scheme with standard renormalization procedures

Predicted finite parts of loop contributions for improved cosmological analysis

Abstract

The effective field theory of large-scale structure allows for a consistent perturbative bias expansion of the rest-frame galaxy density field. In this work, we present a systematic approach to renormalize galaxy bias and stochastic parameters using a finite cutoff scale $\Lambda$. We derive the differential equations of the Wilson-Polchinski renormalization group that describe the evolution of the finite-scale bias parameters with $\Lambda$, analogous to the $\beta$-function running in QFT. We further provide the connection between the finite-cutoff scheme and the renormalization procedure for $n$-point functions that has been used as standard in the literature so far; some inconsistencies in the treatment of renormalized bias in current EFT analyses are pointed out as well. The fixed-cutoff scheme allows us to predict, in a principled way, the finite part of loop contributions which is due to perturbative modes and which, in the standard renormalization approach, is absorbed into counterterms. We expect that this will allow for the robust extraction of (a yet-to-be-determined amount of) additional cosmological information from galaxy clustering, both when using field-level techniques and $n$-point functions.