Clustering of dark matter tracers: Renormalizing the bias parameters

By P. Mcdonald. 2006

145 citations recorded by the source corpus.

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

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Citations in the corpus

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality (2014, methodology): “Various techniques to improve upon the PT are suggested: Renormalization group approach [168], Resumming perturbation [169], Renormalized Perturbation”
Renormalized halo bias (2014, methodology): “In the process, we have clarified a few technical aspects of the renormalization procedure proposed by McDonald [13].”
The DESI Experiment Part I: Science,Targeting, and Survey Design (2016, background): “The physics of how they trace the dark matter fluctuations is well understood based on arguments about locality of galaxy formation [54, 55, 56].”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological implications of the configuration-space clustering wedges (2016, background): “(A15) The term Pb2b2 does not reduce to zero at low-k; therefore, we renormalize that limit as (McDonald 2006) Pb2b2 (k) = 1 2 ∫ ( 1 − P (q) P (k − q) ) P (k − q)P (q)d3q, (A16) which now reduces to zero as k2.”
The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias (2007, background): “The use of highly biased tracers, such as luminous red galaxies at lower z and Lyman break galaxies or Lyman-α emitters at higher z requires a reliable modelling of non-linearity and scale-dependence of galaxy bias, even at relatively large spatial scales (Smith et al. 2006, 2007; McDonald 2006).”
The Lyman-α forest in three dimensions: measurements of large scale flux correlations from BOSS 1st-year data (2011, background): “Unfortunately, as shown by [81, 82], this linearized calculation is mathematically nonsensical.”
How to evade the sample variance limit on measurements of redshift-space distortions (2008, background): “renormalization of perturbation theory that local non-linear transformations of the density field can do nothing but change the bias parameters on large scales [22, 31, 32].”
Inflation and the scale dependent spectral index: prospects and strategies (2010, background): “At the level of the Fisher matrix, we have found that accounting for third order bias parameters, of the form detailed in [69], degrades the constraints on ns and αs by a factor of ∼ 2.”
Large-scale bias and efficient generation of initial conditions for nonlocal primordial non-Gaussianity (2011, background): “In this case, however, there is the extra complication in going from the bias parameters in the expansion of perturbations to the bias parameters that appear in the correlators such as the power spectrum, which will differ in general by renormalizations induced by loop corrections [52, 77, 78].”