Peak-Background Split, Renormalization, and Galaxy Clustering

Abstract

We present a derivation of two-point correlations of general tracers in the peak-background split (PBS) framework by way of a rigorous definition of the PBS argument. Our expressions only depend on connected matter correlators and "renormalized" bias parameters with clear physical interpretation, and are independent of any coarse-graining scale. This result should be contrasted with the naive expression derived from a local bias expansion of the tracer number density with respect to the matter density perturbation δ_L coarse-grained on a scale R_L. In the latter case, the predicted tracer correlation function receives contributions of order <δ_L^n> at each perturbative order n, whereas, in our formalism, these are absorbed in the PBS bias parameters at all orders. Further, this approach naturally predicts both a scale-dependent bias ~ k^2 such as found for peaks of the density field, and the scale-dependent bias induced by primordial non-Gaussianity in the initial conditions. The only assumption made about the tracers is that their abundance at a given position depends solely on the matter distribution within a finite region around that position.

25 pages, 1 figure, 1 table; v2: expanded on case of univ. mass functions (Sec II C) and connection to multipoint propagators; v3: minor edits and clarifications, matches PRD published version

References in corpus (17)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Gravity and Large-Scale Non-local Bias
• The bispectrum of galaxies from high-redshift galaxy surveys: primordial non-Gaussianity and non-linear galaxy bias
• Multi-Point Propagators in Cosmological Gravitational Instability
• Primordial non-Gaussianity: large-scale structure signature in the perturbative bias model
• Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity
• Primordial non-Gaussianity, scale-dependent bias, and the bispectrum of galaxies
• Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields
• Large-scale BAO signatures of the smallest galaxies
• 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
• Multi-Point Propagators for Non-Gaussian Initial Conditions
• A local bias approach to the clustering of discrete density peaks
• Halo Sampling, Local Bias and Loop Corrections
• Lagrangian bias in the local bias model

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