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Astron. Astrophys. 331, 829-837 (1998)

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The skewness and kurtosis of the projected density distribution function: validity of perturbation theory

E. Gaztañaga 1, 2 and F. Bernardeau 3

1 Institut d'Estudis Espacials de Catalunya, Unidad Nixta del CSIC, Edf. Nexus-104 - c/ Gran Capitan 2-4, E-08034 Barcelona, Spain
2 NASA/Fermilab Astrophysics Center, Fermilab, Batavia, IL 60510, USA
3 Service de Physique Théorique, C.E. de Saclay, F-91191 Gif-sur-Yvette cedex, France

Received 17 July 1997 / Accepted 10 November 1997


We study the domain of validity of Perturbation Theory (PT), by comparing its predictions for the reduced skewness, [FORMULA], and kurtosis, [FORMULA], of the projected cosmological density field, with the results of N-body simulations. We investigate models with different linear power spectra and consider as physical applications both angular galaxy catalogues and weak lensing surveys. We first find that the small-angle approximation for the predicted skewness provides a good match to the exact numerical PT results. On the other hand, results from non-linear simulated catalogues agree well with PT results on quasi-linear angular scales, which correspond to scales larger than about [FORMULA] in the applications we have considered. We also point out that projection effects tend to attenuate the effects of strong non-linearities in the angular skewness and kurtosis.

Key words: cosmic microwave background – dark matter – gravitational lensing – large-scale structure of Universe

Send offprint requests to: F. Bernardeau (fbernardeau@cea.fr)

© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998