Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

Hamilton, A.; Kumar, Piyush; Lu, Edward T.; Matthews, A.

doi:10.1086/186057

Cited by 343 publications

(487 citation statements)

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“…The power spectrum of the density fluctuations is described by its primordial slope of n = 1, a shape parameter Γ = 0.21, and a normalization of σ 8 = 1. We used the fit formula of Bardeen et al (1986) for the linear power spectrum, and the prescription of Hamilton et al (1991) in the form given in Peacock & Dodds (1996) to describe the non-linear evolution of the power spectrum 1 . Furthermore, we fix the survey properties to be described by a fiducial area of A = 1 deg 2 , a number density n = 30 arcmin −2 of source galaxies, and an intrinsic ellipticity dispersion of σ = 0.3.…”

Section: Averaging Over An Ensemble Of Galaxy Positionsmentioning

confidence: 99%

Analysis of two-point statistics of cosmic shear

Schneider

Waerbeke

Kilbinger

et al. 2002

A&A

223

354

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Abstract.Recently, cosmic shear, the weak lensing effect by the inhomogeneous matter distribution in the Universe, has not only been detected by several groups, but the observational results have been used to derive constraints on cosmological parameters. For this purpose, several cosmic shear statistics have been employed. As shown recently, all second-order statistical measures can be expressed in terms of the two-point correlation functions of the shear, which thus represents the basic quantity; also, from a practical point-of-view, the two-point correlation functions are easiest to obtain from observational data which typically have complicated geometry. We derive in this paper expressions for the covariance matrix of the cosmic shear twopoint correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry which allows us to obtain approximations for the covariance matrix in terms of integrals which are readily evaluated numerically. These results are then used to study the covariance of the aperture mass dispersion which has been employed earlier in quantitative cosmic shear analyses. We show that the aperture mass dispersion, measured at two different angular scales, quickly decorrelates with the ratio of the scales. Inverting the relation between the shear two-point correlation functions and the power spectrum of the underlying projected matter distribution, we construct estimators for the power spectrum and for the band powers, and show that they yields accurate approximations; in particular, the correlation between band powers at different wave numbers is quite weak. The covariance matrix of the shear correlation function is then used to investigate the expected accuracy of cosmological parameter estimates from cosmic shear surveys. Depending on the use of prior information, e.g. from CMB measurements, cosmic shear can yield very accurate determinations of several cosmological parameters, in particular the normalization σ 8 of the power spectrum of the matter distribution, the matter density parameter Ω m , and the shape parameter Γ.

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Section: Averaging Over An Ensemble Of Galaxy Positionsmentioning

confidence: 99%

Analysis of two-point statistics of cosmic shear

Schneider

Waerbeke

Kilbinger

et al. 2002

A&A

223

354

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“…One of the most important applications of the conventional self-similar solution is the Ðtting formula for the nonlinear power spectrum by Peacock & Dodds (1996), which is based on an idea originally proposed by Hamilton et al (1991). In the strongly nonlinear regime, on which we focus in this paper, the Peacock-Dodds formula agrees well with the simulations for and also for and ) 0 \ 1, ) 0 \ 1 ) 0 We have found, however, that in and ] j 0 \ 1. )…”

Section: Discussionmentioning

confidence: 99%

“…This solution has been widely applied in modeling the nonlinear gravitational clustering (Hamilton et al 1991 ;Peacock & Dodds 1994, 1996Jain, Mo, & White 1995) and in understanding the pairwise velocity dispersions, and thus the redshift-space distortion (Suto & Jing 1997 ;Jing, Mo, & 1998). In fact, the above prescription has been Borner applied even in cases where the universe is not described by the EinsteinÈde Sitter model and/or the linear power spectrum is not of a power-law form.…”

Section: Introductionmentioning

confidence: 99%

Quasi–Self‐Similar Evolution of the Two‐Point Correlation Function: Strongly Nonlinear Regime in Ω₀< 1 Universes

Suginohara¹,

Taruya²,

Suto³

2002

ApJ

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The well-known self-similar solution for the two-point correlation function of the density Ðeld is valid only in an EinsteinÈde Sitter universe. We attempt to extend the solution for nonÈEinsteinÈde Sitter universes. For this purpose we introduce an idea of quasiÈself-similar evolution ; this approach is based on the assumption that the evolution of the two-point correlation is a succession of stages of evolution, each of which spans a short enough period to be considered approximately self-similar. In addition, we assume that clustering is stable on scales where a physically motivated "" virialization condition ÏÏ is satisÐed. These assumptions lead to a deÐnite prediction for the behavior of the two-point correlation function in the strongly nonlinear regime. We show that the prediction agrees well with N-body simulations in nonÈEinsteinÈde Sitter cases and discuss some remaining problems.

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“…One can interpolate between the linear and highly non-linear regimes to produce semi-analytic models for clustering in the quasi-linear regime which can then be accurately fit to results from N -body simulations (Hamilton 1991;Jain, Mo, & White 1995;Peacock & Dodds 1996). Following the discussion of PD, we define the dimensionless power spectrum as…”

Section: Inferring Spatial Informationmentioning

confidence: 99%

Probing Density Fluctuations Using the First Radio Survey

Cress¹

1998

Observational Cosmology

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Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

Cited by 343 publications

References 0 publications

Analysis of two-point statistics of cosmic shear

Analysis of two-point statistics of cosmic shear

Quasi–Self‐Similar Evolution of the Two‐Point Correlation Function: Strongly Nonlinear Regime in Ω₀< 1 Universes

Probing Density Fluctuations Using the First Radio Survey

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Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

Cited by 343 publications

References 0 publications

Analysis of two-point statistics of cosmic shear

Analysis of two-point statistics of cosmic shear

Quasi–Self‐Similar Evolution of the Two‐Point Correlation Function: Strongly Nonlinear Regime in Ω0< 1 Universes

Probing Density Fluctuations Using the First Radio Survey

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Product

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Quasi–Self‐Similar Evolution of the Two‐Point Correlation Function: Strongly Nonlinear Regime in Ω₀< 1 Universes