Bias in the Effective Field Theory of Large Scale Structures

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 $k/k_{\mathrm{NL}}$ and $k/k_{\mathrm{M}}$, where $k$ is the wavenumber of interest, $k_{\mathrm{NL}}$ is the wavenumber associated to the non-linear scale, and $k_{\mathrm{M}}$ is the comoving wavenumber enclosing the mass of a galaxy.

45 pages; v2: added explanations, minor corrections and references

References in corpus (11)

• The Effective Field Theory of Inflation
• The Effective Field Theory of Cosmological Large Scale Structures
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• The IR-resummed Effective Field Theory of Large Scale Structures
• The Scale Dependence of Halo and Galaxy Bias: Effects in Real Space
• Renormalized Halo Bias
• Biased Tracers and Time Evolution
• The Bispectrum in the Effective Field Theory of Large Scale Structure
• Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity
• The One-Loop Matter Bispectrum in the Effective Field Theory of Large Scale Structures
• Non-local halo bias with and without massive neutrinos

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