Scale-dependent bias and the halo model

Schulz, Alexia; White, Martin

doi:10.1016/j.astropartphys.2005.11.007

Cited by 48 publications

(51 citation statements)

References 23 publications

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“…Within the halo model, the linear regime corresponds to the 2-halo term of clustering between dark matter halos, while the nonlinear regime involves the 1-halo term of the profile and concentration within a halo. For k ≈ 0.2−1h Mpc −1 , the 1-halo contribution may be approximated by a white noise term in the power spectrum [27], due to Poisson fluctuations in the number of halos. In other words,…”

Section: B Uncertainty and Biasmentioning

confidence: 99%

Separating dark physics from physical darkness: Minimalist modified gravity versus dark energy

2007

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The acceleration of the cosmic expansion may be due to a new component of physical energy density or a modification of physics itself. Mapping the expansion of cosmic scales and the growth of large scale structure in tandem can provide insights to distinguish between the two origins. Using Minimal Modified Gravity (MMG) -a single parameter gravitational growth index formalism to parameterize modified gravity theories -we examine the constraints that cosmological data can place on the nature of the new physics. For next generation measurements combining weak lensing, supernovae distances, and the cosmic microwave background we can extend the reach of physics to allow for fitting gravity simultaneously with the expansion equation of state, diluting the equation of state estimation by less than 25% relative to when general relativity is assumed, and determining the growth index to 8%. For weak lensing we examine the level of understanding needed of quasiand nonlinear structure formation in modified gravity theories, and the trade off between stronger precision but greater susceptibility to bias as progressively more nonlinear information is used.

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Section: B Uncertainty and Biasmentioning

confidence: 99%

Separating dark physics from physical darkness: Minimalist modified gravity versus dark energy

2007

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“…Pairs of galaxies can be separated as one-or two-halo, i.e., occupying the same or distinct dark matter halos. As discussed in Seljak (2000) and Schulz & White (2006), scale dependence of the bias between galaxies and dark matter arises primarily because the one-halo galaxy term is enhanced relative to the dark matter more than the two-halo term. The Huff et al (2007) configuration space band-power estimator provides a promising avenue to combat this effect: it confines the uncertainty in small-scale power, including the one-halo contribution, to an additive term of known functional form.…”

Section: Introductionmentioning

confidence: 99%

Luminous Red Galaxy Halo Density Field Reconstruction and Application to Large-Scale Structure Measurements

Reid¹,

Spergel²,

Bode³

2009

ApJ

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The nontrivial relationship between observations of galaxy positions in redshift space and the underlying matter field complicates our ability to determine the linear theory power spectrum and extract cosmological information from galaxy surveys. The Sloan Digital Sky Survey (SDSS) luminous red galaxy (LRG) catalog has the potential to place powerful constraints on cosmological parameters. LRGs are bright, highly biased tracers of largescale structure. However, because they are highly biased, the nonlinear contribution of satellite galaxies to the galaxy power spectrum is large and fingers-of-God (FOGs) are significant. The combination of these effects leads to a ∼10% correction in the underlying power spectrum at k = 0.1 h Mpc −1 and ∼40% correction at k = 0.2 h Mpc −1 in the LRG P (k) analysis of Tegmark et al., thereby compromising the cosmological constraints when this potentially large correction is left as a free parameter. We propose an alternative approach to recovering the matter field from galaxy observations. Our approach is to use halos rather than galaxies to trace the underlying mass distribution. We identify FOGs and replace each FOG with a single halo object. This removes the nonlinear contribution of satellite galaxies, the one-halo term. We test our method on a large set of high-fidelity mock SDSS LRG catalogs and find that the power spectrum of the reconstructed halo density field deviates from the underlying matter power spectrum at the 1% level for k 0.1 h Mpc −1 and 4% at k = 0.2 h Mpc −1 . The reconstructed halo density field also removes the bias in the measurement of the redshift space distortion parameter β induced by the FOG smearing of the linear redshift space distortions.

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“…where b 0 is a constant galaxy bias factor and P R (k) denotes the real-space galaxy power spectrum (Coles 1993;Fry & Gaztañaga 1994;Weinberg 1995;Mann et al 1998;Scherrer & Weinberg 1998;Narayanan et al 2000;Schulz & White 2006). The additive "shot noise" term 6 Menzel Fellow.…”

Section: Introductionmentioning

confidence: 99%

Extending Recovery of the Primordial Matter Power Spectrum

Yoo

Weinberg

Tinker

et al. 2009

ApJ

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The shape of the primordial matter power spectrum encodes critical information on cosmological parameters. At large scales, in the linear regime, the observable galaxy power spectrum P obs (k) is expected to follow the shape of the linear matter power spectrum P lin (k), but on smaller scales the effects of nonlinearity and galaxy bias make the ratio P obs (k)/P lin (k) scale dependent. We develop a method that can extend the dynamic range of the primordial matter power spectrum recovery, taking full advantage of precision measurements on quasi-linear scales, by incorporating additional constraints on the galaxy halo occupation distribution (HOD) from the projected galaxy correlation function w p (r p ). We devise an analytic model to calculate observable galaxy power spectrum P obs (k) in real space and redshift space, given P lin (k) and HOD parameters, and we demonstrate its accuracy at the few percent level with tests against a suite of populated N-body simulations. Once HOD parameters are determined by fitting w p (r p ) measurements for a given cosmological model, galaxy bias is completely specified, and our analytic model predicts both the shape and normalization of P obs (k). Applying our method to the main galaxy redshift samples from the Sloan Digital Sky Survey (SDSS), we find that the real-space galaxy power spectrum follows the shape of the nonlinear matter power spectrum at the 1%-2% level up to k = 0.2 h Mpc −1 and that current observational uncertainties in HOD parameters leave only few percent uncertainties in our scale-dependent bias predictions up to k = 0.5 h Mpc −1 . These uncertainties can be marginalized over in deriving cosmological parameter constraints, and they can be reduced by higher precision w p (r p ) measurements. When we apply our method to the SDSS luminous red galaxy (LRG) samples, we find that the linear bias approximation is accurate to 5% at k 0.08 h Mpc −1 , but the strong scale dependence of LRG bias prevents the use of linear theory at k 0.08 h Mpc −1 . Our HOD model prediction is in good agreement with the recent SDSS LRG power spectrum measurements at all measured scales (k 0.2 h Mpc −1 ), naturally explaining the observed shape of P obs (k) in the quasi-linear regime. The phenomenological "Q-model" prescription is a poor description of galaxy bias for the LRG samples, and it can lead to biased cosmological parameter estimates when measurements at k 0.1 h Mpc −1 are included in the analysis. We quantify the potential bias and constraints on cosmological parameters that arise from applying linear theory and Q-model fitting, and we demonstrate the utility of HOD modeling of highprecision measurements of P obs (k) on quasi-linear scales, which will be obtainable from the final SDSS data set.

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Scale-dependent bias and the halo model

Cited by 48 publications

References 23 publications

Separating dark physics from physical darkness: Minimalist modified gravity versus dark energy

Separating dark physics from physical darkness: Minimalist modified gravity versus dark energy

Luminous Red Galaxy Halo Density Field Reconstruction and Application to Large-Scale Structure Measurements

Extending Recovery of the Primordial Matter Power Spectrum

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