Incompatibility of Standard Galaxy Bias Models in General Relativity

TL;DR

This paper shows that existing Newtonian-based galaxy bias models are incompatible with general relativity and introduces the need for a covariant, diffeomorphism-compatible model to accurately interpret galaxy clustering data.

Contribution

The paper demonstrates the incompatibility of standard galaxy bias models with general relativity and emphasizes developing a covariant framework respecting diffeomorphism symmetry.

Findings

Reverse-engineered approaches violate diffeomorphism invariance

Standard models are incompatible with relativistic symmetry

Implications for primordial non-Gaussianity measurements

Abstract

The standard model for galaxy bias is built in a Newtonian framework, and several attempts have been made in the past to put it in a relativistic framework. The focus of past works was, however, to use the same Newtonian formulation, but to provide its interpretation in a relativistic framework by either fixing a gauge condition or transforming to a local coordinate system. Here we demonstrate that these reverse-engineered approaches do not respect the diffeomorphism symmetry in general relativity, and we need to develop a covariant model of galaxy bias that is diffeomorphism compatible. We consider a simple toy model for galaxy bias and discuss the impact for measuring the primordial non-Gaussianity.