Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture

By Takahiko Matsubara. 2008

216 citations recorded by the source corpus.

The nonlinear perturbation theory of gravitational instability is extended to include effects of both biasing and redshift-space distortions, which are inevitable in predicting observable quantities in galaxy surveys. Weakly nonlinear effects in galaxy clustering on large scales recently attracted great interest, since the precise determination of scales of baryon acoustic oscillations is crucial to investigate the nature of dark energy by galaxy surveys. We find that a local Lagrangian bias and redshift-space distortions are naturally incorporated in our formalism of perturbation theory with a resummation technique via the Lagrangian picture. Our formalism is applicable to any biasing scheme which is local in Lagrangian space, including the halo bias as a special case. Weakly nonlinear effects on halo clustering in redshift space are analytically given. We assume only a fundamental idea of the halo model: haloes form according to the extended Press-Schechter theory, and the spatial distributions are locally biased in Lagrangian space. There is no need for assuming the spherical collapse model to follow the dynamical evolution, which is additionally assumed in standard halo prescriptions. One-loop corrections to the power spectrum and correlation function of haloes in redshift space are explicitly derived and presented. Instead of relying on expensive numerical simulations, our approach provides an analytic way of investigating the weakly nonlinear effects, simultaneously including the nonlinear biasing and nonlinear redshift-space distortions. Nonlinearity introduces a weak scale dependence in the halo bias. The scale dependence is a smooth function in Fourier space, and the bias does not critically change the feature of baryon acoustic oscillations in the power spectrum. The same feature in the correlation function is less affected by nonlinear effects of biasing.

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Citations in the corpus

The clustering of the SDSS main galaxy sample – II. Mock galaxy catalogues and a measurement of the growth of structure from redshift space distortions at z = 0.15 (2014, methodology): “From Matsubara (2008), we can easily relate the linear galaxy bias, b, to the first derivative of the Lagrangian bias function by 〈F′〉 = b − 1.”
The clustering of galaxies in the sdss-iii baryon oscillation spectroscopic survey: Baryon acoustic oscillations in the data release 9 spectroscopic galaxy sample (2012, background): “…is caused by matter flows and peculiar velocities on intermediate scales (∼20 h−1 Mpc), which act to suppress small-scale oscillations in the galaxy power spectrum and smooth the BAO feature in the correla- tion function (Eisenstein et al. 2007b; Crocce & Scoccimarro 2008; Matsubara 2008a,b).”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Testing gravity with redshift-space distortions using the power spectrum multipoles (2013, methodology): “…to modelling the power spectrum or correlation function of the anisotropic galaxy clustering have been suggested in recent years (Scoccimarro 2004; Matsubara 2008a,b, 2011, 2013; Carlson, White & Padmanabhan 2009; Taruya, Nishimichi & Saito 2010; Reid & White 2011; Seljak & McDonald 2011; Vlah et…”
The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measurement of the growth rate of structure from the anisotropic correlation function between redshift 0.8 and 2.2 (2018, methodology): “CLPT gives predictions for tracers that are biased in a local Lagrangian formalism developed by Matsubara (2008b) where the tracer density field, δtracer, is assumed to be a function, F, of a smoothed linear matter field δm,R at the same Lagrangian position q: 1 + δtracer(q) = F [δm,R(q)] , (22)…”
Cosmological non-linearities as an effective fluid (2010, background): “Our work builds on a long history of studies in non-linear perturbation theory [23, 24, 25, 26, 27, 28, 29, 30, 31, 2], numerical simulations [32, 33, 34, 35], and effective field theory [5, 6, 8, 37].”
The clustering of galaxies in the SDSS‐III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large‐scale two‐point correlation function (2012, background): “…progress regarding the theoretical understanding of the effects of non-linear evolution, which can now be accurately modelled (Crocce & Scoccimarro 2006; Matsubara 2008a,b; Taruya et al. 2009), and even partially corrected for (Eisenstein et al. 2007; Seo et al. 2010; Padmanabhan et al. 2012).”
The Zel'dovich approximation (2014, methodology): “The correlation function within the Zel’dovich approximation then follows by elementary manipulations (Bond & Couchman 1988; Fisher & Nusser 1996; Matsubara 2008a,b; Carlson, Reid & White 2013; Wang, Reid & White 2013; Tassev 2014b).”
Interpreting large-scale redshift-space distortion measurements (2011, unknown): “…is a damping on small scales, which can be well approximated by a Gaussian smoothing (Bharadwaj 1996; Crocce & Scoccimarro 2006, 2008; Eisenstein, Seo & White 2007; Matsubara 2008a,b) P nlbao(k, µ) = P lin bao(k, µ) × exp ( −k2 [ (1− µ2)Σ⊥ 2 + µ2Σ|| 2 ]) , (16) where Σ⊥ = Σ0G and Σ|| = Σ0G(1 + f).”
Extragalactic science, cosmology, and Galactic archaeology with the Subaru Prime Focus Spectrograph (2012, methodology): “(Matsubara 2008; Taruya et al. 2009; Nishimichi & Taruya 2011; Tang et al. 2011; Hikage et al. 2012a,b).”
Cosmological constraints from the clustering of the Sloan Digital Sky Survey DR7 luminous red galaxies (vol 404, pg 60, 2010) (2009, background): “(B3) For our adopted fiducial cosmological model, we find σ logM ∼ 0.6–0.9 in order to match the amplitude of the observed largescale clustering of the LRGs; the exact parameter values used to generate the mock catalogues are given in Reid et al. (2009).”
The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations (2011, methodology): “…the damping of the baryon acoustic peak caused by the displacement of matter due to bulk flows (Eisenstein et al. 2007, Crocce & Scoccimarro 2008, Matsubara 2008) by interpolating between the linear and reference power spectra using a Gaussian damping term g(k) ≡ exp (−k2σ2v): Pdamped(k) =…”
Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample (2013, methodology): “In the present paper, among several proposed models to account for the non-linear RSDs ((Matsubara 2008b; Reid & White 2011; Seljak & McDonald 2011)), we adopt the model given by (Taruya et al. 2010d) (hereafter, TNS model): P s(k, µ) = DFoG(kµfσv) × [ PKaiser(k, µ; f) +A(k, µ; f) +B(k, µ; f) ] ,…”
Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample (2009, background): “The primary consequence is a damping on small scales, which can be well approximated by a Gaussian smoothing (Bharadwaj 1996; Crocce & Scoccimarro 2006, 2008; Eisenstein et al. 2007; Matsubara 2008a,b).”
Bias in the effective field theory of large scale structures (2014, background): “The Lagrangian approach to biased objects has been developed for quite some time in, for example, [12, 17, 19, 20].”
A 2 per cent distance to $z$=0.35 by reconstructing baryon acoustic oscillations - I. Methods and application to the Sloan Digital Sky Survey (2012, background): “This smoothing is well understood (Eisenstein et al. 2007b; Crocce & Scoccimarro 2008; Matsubara 2008a,b; Padmanabhan & White 2009; Seo et al. 2010) and is physically caused by large-scale flows.”
The cosmological analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure (2019, background): “few of the perturbative approaches that were developed prior to the EFTofLSS and that were essential for the development of the EFTofLSS, and we list a very-small sample of the relevant references: Zeldovich approximation [11], SPT [14, 15], LPT [16], RPT [17], MPTbreeze [18, 19], RegPT [20], CLPT [”