Bias in the Effective Field Theory of Large Scale Structures

TL;DR

The paper addresses how to describe biased tracers like galaxies within the EFTofLSS, highlighting that galaxy overdensity is determined by initial dark matter fields and is non-local in time in Eulerian formulations. It develops a Lagrangian bias framework that tracks the formation region of collapsed objects, enabling IR-resummation and a perturbative series that is manifestly convergent in $k/k_{\rm NL}$ and $k/k_{\rm M}$. The work provides explicit one-loop expressions for dark-matter–galaxy cross-correlations, details the renormalization of bias coefficients to remove UV sensitivity, and shows that a quasi-local in time approximation can reduce the number of independent bias parameters while maintaining accuracy. These results lay the groundwork for high-precision predictions of galaxy clustering and cross-correlations, with direct implications for interpreting next-generation large-scale structure surveys. Future work will compare these predictions with simulations and observations to calibrate bias parameters and assess the trade-off between parameter count and predictive power, extending to higher-order statistics like the bispectrum.

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.