Higher order moments of the density field in a parametrized sequence of non-Gaussian theories

White, Martin

doi:10.1046/j.1365-8711.1999.02951.x

Cited by 23 publications

(24 citation statements)

References 47 publications

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“…In addition, a number of studies considered the evolution of higher-order moments from non-Gaussian initial conditions given by cosmic strings [146,9] and texture models [252] using numerical simulations. Recently, measurements of higherorder moments in numerical simulations with χ 2 N initial conditions with N degrees of freedom were given in [689]. General properties of one-point moments evolved from non-Gaussian initial conditions were considered using PT in [238,333,124,255,195].…”

Section: Evolution From Non-gaussian Initial Conditionsmentioning

confidence: 99%

Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver.

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Section: Evolution From Non-gaussian Initial Conditionsmentioning

confidence: 99%

Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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“…We assume, using the arguments of Refs. [41][42][43] (see also Ref. [39]), that PDF of the smoothed ζ field can be expressed in the form…”

Section: Pbh Constraintsmentioning

confidence: 99%

Axion inflation with gauge field production and primordial black holes

2014

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We study the process of primordial black hole (PBH) formation at the beginning of radiation era for the cosmological scenario in which the inflaton is a pseudo-Nambu-Goldstone boson (axion) and there is a coupling of the inflaton with some gauge field. In this model inflation is accompanied by the gauge quanta production and a strong rise of the curvature power spectrum amplitude at small scales (along with non-Gaussianity) is predicted. We show that data on PBH searches can be used for a derivation of essential constraints on the model parameters in such an axion inflation scenario. We compare our numerical results with the similar results published earlier, in the work by Linde et al.Comment: v2: 18 pages, 5 figures. Revised version of the paper accepted for publication in Phys.Rev.

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“…The chi-squared distribution has the added attractive feature that the reduced PDF remains approximately the same when smoothed on a variety of length-scales using either Gaussian (GAU) or top-hat (TH) windows (e.g. White 1999). The reduced PDF that results from the smoothing becomes increasingly different from the original as the number of degrees of freedom, n, gets smaller.…”

Section: R E S U Lt Smentioning

confidence: 99%

The cloud-in-cloud problem for non-Gaussian density fields

Avelino

Viana

2000

Monthly Notices of the Royal Astronomical Society

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The cloud-in-cloud problem is studied in the context of the extension to non-Gaussian density fields of the Press-Schechter approach for the calculation of the mass function. As an example of a non-Gaussian probability distribution functions (PDFs) we consider the Chi-square, with various degrees of freedom. We generate density fields in cubic boxes with periodic boundary conditions and then determine the number of points considered collapsed at each scale through an hierarchy of smoothing windows. We find that the mass function we obtain differs from that predicted using the Extended Press-Schechter formalism, particularly for low values of $\sigma$ and for those PDFs most distinct from a Gaussian.Comment: 5 pages, LaTex using mn.sty, matches published version, results for the Inverted Chi-square distribution withdraw

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Higher order moments of the density field in a parametrized sequence of non-Gaussian theories

Cited by 23 publications

References 47 publications

Large-scale structure of the Universe and cosmological perturbation theory

Large-scale structure of the Universe and cosmological perturbation theory

Axion inflation with gauge field production and primordial black holes

The cloud-in-cloud problem for non-Gaussian density fields

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