Measuring bias from unbiased observable

TL;DR

This paper derives an exact analytic function for galaxy bias b(z), enabling more accurate measurements from galaxy surveys and reducing its nuisance status, with solutions applicable across different gravity theories.

Contribution

It provides the first exact analytic form of galaxy bias b(z) that can be directly measured from surveys, including approximate solutions for various gravity theories.

Findings

Exact analytic function of b(z) derived

Bias can be measured using redshift space distortions

Solutions applicable to different gravity models

Abstract

Since Kaiser introduced galaxies as a biased tracer of the underlying total mass field, the linear galaxies bias, b(z) appears ubiquitously both in theoretical calculations and in observational measurements related to galaxy surveys. However, the generic approaches to the galaxy density is a non-local and stochastic function of the underlying dark matter density and it becomes difficult to make the analytic form of b(z). Due to this fact, b(z) is known as a nuisance parameter and the effort has been made to measure bias free observable quantities. We provide the exact and analytic function of b(z) which also can be measured from galaxy surveys using the redshift space distortions parameters, more accurately unbiased observable \beta \sigma_{\rm{gal}} = f \sigma_8. We also introduce approximate solutions for b(z) for different gravity theories. One can generalize these approximate solutions to be exact when one solves the exact evolutions for the dark matter density fluctuation of given gravity theories. These analytic solutions for b(z) make it advantage instead of nuisance.