Bias in the Effective Field Theory of Large Scale Structures

TL;DR

This paper develops a refined theoretical framework within the Effective Field Theory of Large Scale Structures to better describe galaxy bias, incorporating Lagrangian and Eulerian perspectives, and addresses renormalization for improved convergence.

Contribution

It introduces a Lagrangian space description for galaxy bias in EFT, upgrades Eulerian calculations, and discusses renormalization to ensure convergence of galaxy correlation functions.

Findings

Eulerian theory is perturbatively local in space but non-local in time.

The theory can be considered quasi time-local with specific operator structures.

Renormalization of bias coefficients leads to a convergent series for galaxy correlations.

Abstract

We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what recently done for dark matter, we show how this Lagrangian space description can be recovered by upgrading simpler Eulerian calculations. We describe the Eulerian theory. We show that it is perturbatively local in space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. We describe renormalization of the bias coefficients so that, after this and after upgrading the Eulerian calculation to a Lagrangian one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of $k/k_{\rm NL}$ and $k/k_{\rm M}$, where $k$ is the wavenumber of interest, $k_{\rm NL}$ is the wavenumber associated to the non-linear scale, and $k_{\rm M}$ is the comoving wavenumber enclosing the mass of a galaxy.