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Non Gaussian Minkowski functionals and extrema counts for CMB maps

Published online by Cambridge University Press:  12 October 2016

Dmitri Pogosyan ,
Sandrine Codis  and
Christophe Pichon
Dmitri Pogosyan
Affiliation:
Department of Physics, University of Alberta, 11322-89 Avenue, Edmonton, Alberta, T6G 2G7, Canada CNRS, UPMC, Institut d'astrophysique de Paris, 98 bis boulevard Arago, 75014, Paris, France CNRS, Institut Lagrange de Paris, 98 bis boulevard Arago, 75014, Paris, France
Sandrine Codis
Affiliation:
CNRS, UPMC, Institut d'astrophysique de Paris, 98 bis boulevard Arago, 75014, Paris, France
Christophe Pichon
Affiliation:
CNRS, UPMC, Institut d'astrophysique de Paris, 98 bis boulevard Arago, 75014, Paris, France
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Abstract

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In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating the effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.

Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 11 , Symposium S308: The Zeldovich Universe: Genesis and Growth of the Cosmic Web , June 2014 , pp. 61 - 66
Copyright
Copyright © International Astronomical Union 2016 

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