Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS

By P. Mcdonald, A. Roy. 2009

355 citations recorded by the source corpus.

On very large scales, density fluctuations in the Universe are small, suggesting a perturbative model for large-scale clustering of galaxies (or other dark matter tracers), in which the galaxy density is written as a Taylor series in the local mass density, δ, with the unknown coefficients in the series treated as free ``bias'' parameters. We extend this model to include dependence of the galaxy density on the local values of ∇i∇j and ∇ivj, where is the potential and v is the peculiar velocity. We show that only two new free parameters are needed to model the power spectrum and bispectrum up to 4th order in the initial density perturbations, once symmetry considerations and equivalences between possible terms are accounted for. One of the new parameters is a bias multiplying sijsji, where sij = [∇i∇j∇−2−(1/3)δKij]δ. The other multiplies sijtji, where tij = [∇i∇j∇−2−(1/3)δKij](θ−δ), with θ = −(a H dln D/dln a)−1∇v. (There are other, observationally equivalent, ways to write the two terms, e.g., using θ−δ instead of sijsji.) We show how short-range (non-gravitational) non-locality can be included through a controlled series of higher derivative terms, starting with R2∇2δ, where R is the scale of non-locality (this term will be a small correction as long as k2R2 is small, where k is the observed wavenumber). We suggest that there will be much more information in future huge redshift surveys in the range of scales where beyond-linear perturbation theory is both necessary and sufficient than in the fully linear regime.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ec2e628580e385a6be980bfe3b6f7025a9a6f52f

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Citations in the corpus

Consistent modeling of velocity statistics and redshift-space distortions in one-loop perturbation theory (2020, methodology): “In this paper we shall consider 1-loop perturbation theory in both the Eulerian (EPT; [16–27]) and Lagrangian (LPT; [28–39]) formulations, and their extensions as an effective field theories [39–41].”
Primordial non-Gaussianity from the large-scale structure (2010, background): “Models of galaxy clustering assume for instance that the galaxy biasing relation only depends on the local mass density, but the actual biasing could be more complex [80, 81].”
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].”
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].”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release (2015, background): “Non-local bias has been recently found to be relevant (McDonald & Roy 2009; Baldauf et al. 2012; Chan, Scoccimarro & Sheth 2012; Sheth, Chan & Scoccimarro 2013; Saito et al. 2014).”
Bias in the effective field theory of large scale structures (2014, methodology): “When computing quantities in perturbation theory, as explained in detail in [9], one can usefully use the fact that up to a given order in perturbation theory some different quantities turn out to be numerically equal in order to simplify the algebra.”
The cosmological analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure (2019, methodology): “Passing to biased tracers, they have been studied in the context of the EFTofLSS in [9, 47, 48, 49, 50, 51] (see also [52]), the halo power spectrum and bispectrum including all cross correlations with the dark matter field have been studied and compared with simulations in [9, 48].”
Nonlinear perturbation theory extension of the Boltzmann code CLASS (2020, background): “Following the first attempts to build such a description in terms of a local-in-density bias expansion, an important milestone was the realization that various tidal and higher derivative bias operators must also be included [53, 54].”
Gravity and Large-Scale Nonlocal Bias (2012, background): “Based on symmetry arguments [34] suggested a model of non-local bias with similar, but not identical, structure to what is derived here.”
On the statistics of biased tracers in the Effective Field Theory of Large Scale Structures (2015, methodology): “This is arrived at by readjusting the bias parameter so as to cancel the contribution from perturbation theory that is obtained from a regime where it cannot be trusted, and readjusting it so that the effect of short distance physics at long distance is correctly reproduced [20].”
The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from the anisotropic power spectrum of the quasar sample between redshift 0.8 and 2.2 (2020, methodology): “The 1-loop bias terms are taken from McDonald & Roy (2009) and all terms are calculated at 2-loop order following the RegPT scheme (Taruya 2014).”
COSMOLIKE - cosmological likelihood analyses for photometric galaxy surveys (2016, background): “Perturbative models for galaxy biasing in the quasi-linear regime is an active area of research (e.g. McDonald & Roy 2009; Angulo et al. 2015; Senatore 2015), and the model for galaxy clustering and galaxy–galaxy lensing in equation (9) needs to be updated for analyses of galaxy clustering…”
Biased Tracers in Redshift Space in the EFT of Large-Scale Structure (2016, background): “From the equations of motion we find that η(2) = 2 7(s (1))2 − 4 21(δ (1))2 [39, 13, 18], so we can define a parameter ψ that is nonzero starting only at third order, ψ ≡ η − 2 7 s(2) + 4 21 δ(2) .”
The Zel'dovich approximation (2014, background): “Suppose we extend F(δ) to also include a tidal-shear dependence, F(δ, s2), as discussed for example by McDonald & Roy (2009)?”
Testing Inflation with Large Scale Structure: Connecting Hopes with Reality (2014, background): “At late times the matter density field can be schematically written as [132]”