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Title: Clustering of dark matter tracers: Renormalizing the bias parameters

Abstract

A commonly used perturbative method for computing large-scale clustering of tracers of mass density, like galaxies, is to model the tracer density field as a Taylor series in the local smoothed mass density fluctuations, possibly adding a stochastic component. I suggest a set of parameter redefinitions, eliminating problematic perturbative correction terms, that should represent a modest improvement, at least, to this method. As presented here, my method can be used to compute the power spectrum and bispectrum to 4th order in initial density perturbations, and higher order extensions should be straightforward. While the model is technically unchanged at this order, just reparametrized, the renormalized model is more elegant, and should have better convergence behavior, for three reasons: First, in the usual approach the effects of beyond-linear-order bias parameters can be seen at asymptotically large scales, while after renormalization the linear model is preserved in the large-scale limit, i.e., the effects of higher order bias parameters are restricted to relatively high k. Second, while the standard approach includes smoothing to suppress large perturbative correction terms, resulting in dependence on the arbitrary cutoff scale, no cutoff-sensitive terms appear explicitly after my redefinitions (and, relatedly, my correction terms are less sensitive to high-k,more » nonlinear, power). Third, the 3rd order bias parameter disappears entirely, so my model has one fewer free parameter than usual (this parameter was redundant at the order considered). This model predicts no significant modification of the baryonic acoustic oscillation (BAO) signal, in real space, supporting the robustness of BAO as a probe of dark energy, and providing a complete perturbative description over the relevant range of scales.« less

Authors:
 [1]
  1. Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8 (Canada)
Publication Date:
OSTI Identifier:
20864099
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 74; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.74.103512; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BARYONS; CONVERGENCE; CORRECTIONS; COSMOLOGY; DENSITY; DISTURBANCES; ENERGY SPECTRA; FLUCTUATIONS; GALAXIES; MASS; NONLINEAR PROBLEMS; NONLUMINOUS MATTER; OSCILLATIONS; RENORMALIZATION

Citation Formats

McDonald, Patrick. Clustering of dark matter tracers: Renormalizing the bias parameters. United States: N. p., 2006. Web. doi:10.1103/PHYSREVD.74.103512.
McDonald, Patrick. Clustering of dark matter tracers: Renormalizing the bias parameters. United States. https://doi.org/10.1103/PHYSREVD.74.103512
McDonald, Patrick. 2006. "Clustering of dark matter tracers: Renormalizing the bias parameters". United States. https://doi.org/10.1103/PHYSREVD.74.103512.
@article{osti_20864099,
title = {Clustering of dark matter tracers: Renormalizing the bias parameters},
author = {McDonald, Patrick},
abstractNote = {A commonly used perturbative method for computing large-scale clustering of tracers of mass density, like galaxies, is to model the tracer density field as a Taylor series in the local smoothed mass density fluctuations, possibly adding a stochastic component. I suggest a set of parameter redefinitions, eliminating problematic perturbative correction terms, that should represent a modest improvement, at least, to this method. As presented here, my method can be used to compute the power spectrum and bispectrum to 4th order in initial density perturbations, and higher order extensions should be straightforward. While the model is technically unchanged at this order, just reparametrized, the renormalized model is more elegant, and should have better convergence behavior, for three reasons: First, in the usual approach the effects of beyond-linear-order bias parameters can be seen at asymptotically large scales, while after renormalization the linear model is preserved in the large-scale limit, i.e., the effects of higher order bias parameters are restricted to relatively high k. Second, while the standard approach includes smoothing to suppress large perturbative correction terms, resulting in dependence on the arbitrary cutoff scale, no cutoff-sensitive terms appear explicitly after my redefinitions (and, relatedly, my correction terms are less sensitive to high-k, nonlinear, power). Third, the 3rd order bias parameter disappears entirely, so my model has one fewer free parameter than usual (this parameter was redundant at the order considered). This model predicts no significant modification of the baryonic acoustic oscillation (BAO) signal, in real space, supporting the robustness of BAO as a probe of dark energy, and providing a complete perturbative description over the relevant range of scales.},
doi = {10.1103/PHYSREVD.74.103512},
url = {https://www.osti.gov/biblio/20864099}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 74,
place = {United States},
year = {Wed Nov 15 00:00:00 EST 2006},
month = {Wed Nov 15 00:00:00 EST 2006}
}