Lagrangian bias of generic large-scale structure tracers

Abstract

The dark matter halos that host galaxies and clusters form out of initial high-density patches, providing a biased tracer of the linear matter density field. In the simplest local bias approximation, the halo field is treated as a perturbative series in the average overdensity of the Lagrangian patch. In more realistic models, however, additional quantities will affect the clustering of halo-patches, and this expansion becomes a function of several stochastic variables. In this paper, we present a general multivariate expansion scheme that can parametrize the clustering of any biased Lagrangian tracer, given only the variables involved and their symmetry (in our case rotational invariance). This approach is based on an expansion in the orthonormal polynomials associated with the relevant variables, so that no renormalization of the coefficients ever occurs. We provide explicit expression for the series coefficients, or Lagrangian bias parameters, in the case of peaks of the linear density field. As an application of our formalism, we present a simple derivation of the original BBKS formula, and compute the non-Gaussian bias in the presence of a primordial trispectrum of the local shape.

16 pages, v2: minor modifications, version accepted by PRD

References in corpus (12)

• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• Gravity and Large-Scale Non-local Bias
• Primordial non-gaussianity, statistics of collapsed objects, and the Integrated Sachs-Wolfe effect
• Understanding higher-order nonlocal halo bias at large scales by combining the power spectrum with the bispectrum
• Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity
• Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields
• Nonlinear power spectrum in the presence of massive neutrinos: perturbation theory approach, galaxy bias and parameter forecasts
• Non-local Lagrangian bias
• Baryon acoustic signature in the clustering of density maxima
• Perturbation Theory Reloaded II: Non-linear Bias, Baryon Acoustic Oscillations and Millennium Simulation In Real Space
• Non-local halo bias with and without massive neutrinos
• Scale-dependent bias from an inflationary bispectrum: the effect of a stochastic moving barrier

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• Application of peaks theory to the abundance of primordial black holes
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• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Modeling CMB Lensing Cross Correlations with {\sc CLEFT}
• Modeling features in the redshift-space halo power spectrum with perturbation theory
• Impacts of biasing schemes in the one-loop integrated perturbation theory
• The clustering of dark matter halos: scale-dependent bias on quasi-linear scales
• Integrated trispectrum detection from BOSS DR12 NGC CMASS
• Phenomenology of BAO evolution from Lagrangian to Eulerian Space
• Excursion set peaks in energy as a model for haloes
• The statistics of peaks of weakly non-Gaussian random fields: Effects of bispectrum in two- and three-dimensions
• Non-perturbative halo clustering from cosmological density peaks
• On the galaxy 3-point correlation function in Modified Gravity
• The Halo Boltzmann Equation
• Tidal shear and the consistency of microscopic Lagrangian halo approaches
• The large-separation expansion of peak clustering in Gaussian random fields
• Velocity bias and the nonlinear perturbation theory of peaks
• A spherical hydrodynamical model of cosmic voids in ΛCDM and beyond
• The role of energy shear in the collapse of protohaloes
• On the Connection between Field-Level Inference and $n$-point Correlation Functions