Evolution of one-point distributions from Gaussian initial fluctuations

Kofman, Lev; Bertschinger, Edmund; Gelb, James M.; Nusser, Adi; Dekel, Avishai

doi:10.1086/173541

Cited by 170 publications

(273 citation statements)

References 32 publications

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“…The assumed Gaussianity of the velocity Ðeld in the mildly nonlinear regime is supported by simulations (Kofman et al 1994 ;Kudlicki et al 2001) and is veriÐed by the nearly normal distribution of the observed ln (z/d) in our sample.…”

Section: Ikelihood Analysissupporting

confidence: 74%

Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and Principal Component Analysis

Silberman¹,

Dekel²,

Eldar³

et al. 2001

ApJ

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We allow for nonlinear e †ects in the likelihood analysis of galaxy peculiar velocities and obtain D35% lower values for the cosmological density parameter and for the amplitude of mass density ) m Ñuctuations This result is obtained under the assumption that the power spectrum in the linear p 8 ) m 0.6. regime is of the Ñat "CDM model (h \ 0.65, n \ 1, COBE normalized) with only as a free parameter. ) m Since the likelihood is driven by the nonlinear regime, we "" break ÏÏ the power spectrum at (h~1 k b D 0.2 Mpc)~1 and Ðt a power law at This allows for independent matching of the nonlinear behavior k [ k b . and an unbiased Ðt in the linear regime. The analysis assumes Gaussian Ñuctuations and errors and a linear relation between velocity and density. Tests using mock catalogs that properly simulate nonlinear e †ects demonstrate that this procedure results in a reduced bias and a better Ðt. We Ðnd for the Mark III and SFI data and 0.37^0.09, respectively, with and ) m \ 0.32^0.06 p 8 ) m 0.6 \ 0.49^0.06 0.63^0.08, in agreement with constraints from other data. The quoted 90% errors include distance errors and cosmic variance, for Ðxed values of the other parameters. The improvement in the likelihood due to the nonlinear correction is very signiÐcant for Mark III and moderately signiÐcant for SFI.When allowing deviations from "CDM, we Ðnd an indication for a wiggle in the power spectrum : an excess near k D 0.05 (h~1 Mpc)~1 and a deÐciency at k D 0.1 (h~1 Mpc)~1, or a "" cold Ñow.ÏÏ This may be related to the wiggle seen in the power spectrum from redshift surveys and the second peak in the cosmic microwave background (CMB) anisotropy.A s2 test applied to modes of a principal component analysis (PCA) shows that the nonlinear procedure improves the goodness of Ðt and reduces a spatial gradient that was of concern in the purely linear analysis. The PCA allows us to address spatial features of the data and to evaluate and Ðne-tune the theoretical and error models. It demonstrates in particular that the models used are appropriate for the cosmological parameter estimation performed. We address the potential for optimal data compression using PCA.

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Section: Ikelihood Analysissupporting

confidence: 74%

Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and Principal Component Analysis

Silberman¹,

Dekel²,

Eldar³

et al. 2001

ApJ

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“…Coles & Jones (1991) suggested to describe the three-dimensional matter density distribution in our Universe by a log-normal random field. Later, numerical simulations of cosmic structure formation showed that a log-normal field provides indeed a good description of the one-and two-point statistics of the evolved matter density field, even though a point-wise exponential mapping of the initial Gaussian density field does not describe the evolved density field well (Kofman et al 1994;Kayo et al 2001). The one-point probability density function (pdf) of the projected density and lensing convergence are also fitted well by a log-normal pdf (Taruya et al 2002).…”

Section: Introductionmentioning

confidence: 99%

Cosmic shear covariance: the log-normal approximation

Hilbert¹,

Hartlap²,

Schneider³

2011

A&A

106

150

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Context. Accurate estimates of the errors on the cosmological parameters inferred from cosmic shear surveys require accurate estimates of the covariance of the cosmic shear correlation functions. Aims. We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal (Gaussian) statistics, but yield more accurate covariance matrices and parameter errors. Methods. We derive expressions for the cosmic shear covariance under the assumption that the underlying convergence field follows log-normal statistics. We also derive a simplified version of this log-normal approximation by only retaining the most important terms beyond normal statistics. We use numerical simulations of weak lensing to study how well the normal, log-normal, and simplified log-normal approximations as well as empirical corrections to the normal approximation proposed in the literature reproduce shear covariances for cosmic shear surveys. We also investigate the resulting confidence regions for cosmological parameters inferred from such surveys. Results. We find that the normal approximation substantially underestimates the cosmic shear covariances and the inferred parameter confidence regions, in particular for surveys with small fields of view and large galaxy densities, but also for very wide surveys. In contrast, the log-normal approximation yields more realistic covariances and confidence regions, but also requires evaluating slightly more complicated expressions. However, the simplified log-normal approximation, although as simple as the normal approximation, yields confidence regions that are almost as accurate as those obtained from the log-normal approximation. The empirical corrections to the normal approximation do not yield more accurate covariances and confidence regions than the (simplified) log-normal approximation. Moreover, they fail to produce positive-semidefinite data covariance matrices in certain cases, rendering them unusable for parameter estimation. Conclusions. The log-normal or simplified log-normal approximation should be used in favour of the normal approximation for parameter estimation and parameter error forecasts. More generally, any approximation to the cosmic shear covariance should ensure a positive-(semi)definite data covariance matrix.

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“…For each model we will analyse the velocity field defined on a 128 3 mesh. The field is obtained using the same procedure as in Kofman et al (1994). First we interpolated mass and momentum from the particle distribution on a regular cubic grid by means of a Triangular Shaped Cloud (TSC) scheme (see Hockney & Eastwood 1981).…”

Section: General Properties Of Velocity Fieldsmentioning

confidence: 99%

“…Gelb & Bertschinger 1994) and is unable to reproduce the slope of the galaxy angular correlation function obtained from the APM survey (Maddox et al 1990).…”

Section: Introductionmentioning

confidence: 98%

Velocity fields in non-Gaussian cold dark matter models

Lucchin¹,

Matarrese²,

Messina³

et al. 1995

Monthly Notices of the Royal Astronomical Society

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We analyse the large-scale velocity field obtained by N-body simulations of cold dark matter (CDM) models with non-Gaussian primordial density fluctuations, considering models with both positive and negative primordial skewness in the density fluctuation distribution. We study the velocity probability distribution and calculate the dependence of the bulk flow, one-point velocity dispersion and Cosmic Mach Number on the filtering size. We find that the sign of the primordial skewness of the density field provides poor discriminatory power on the evolved velocity field. All non-Gaussian models here considered tend to have lower velocity dispersion and bulk flow than the standard Gaussian CDM model, while the Cosmic Mach Number turns out to be a poor statistic in characterizing the models. Next, we compare the large-scale velocity field of a composite sample of optically selected galaxies as described by the Local Group properties, bulk flow, velocity correlation function and Cosmic Mach Number, with the velocity field of mock catalogues extracted from the N-body simulations. The comparison does not clearly permit to single out a best model: the standard Gaussian model is however marginally preferred by the maximum likelihood analysis.

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Evolution of one-point distributions from Gaussian initial fluctuations

Cited by 170 publications

References 32 publications

Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and Principal Component Analysis

Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and Principal Component Analysis

Cosmic shear covariance: the log-normal approximation

Velocity fields in non-Gaussian cold dark matter models

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