scholarly journals Analytic Minkowski functionals of the cosmic microwave background: Second-order non-Gaussianity with bispectrum and trispectrum

2010 ◽  
Vol 81 (8) ◽  
Author(s):  
Takahiko Matsubara
Keyword(s):  
Cosmic Microwave Background ◽  
Second Order ◽  
Microwave Background ◽  
Minkowski Functionals

scholarly journals Non-Gaussianity and the Cosmic Microwave Background Anisotropies

2010 ◽  
Vol 2010 ◽  
pp. 1-68 ◽  
Author(s):  
N. Bartolo ◽  
S. Matarrese ◽  
A. Riotto
Keyword(s):  
Cosmic Microwave Background ◽  
Initial Conditions ◽  
Second Order ◽  
Basic Knowledge ◽  
Secondary Effects ◽  
Microwave Background ◽  
Numerical Examples ◽  
Many Sources ◽  
The Impact ◽  
Recombination Epoch

We review in a pedagogical way the present status of the impact of non-Gaussianity (NG) on the cosmic microwave background (CMB) anisotropies. We first show how to set the initial conditions at second order for the CMB anisotropies when some primordial NG is present. However, there are many sources of NG in CMB anisotropies, beyond the primordial one, which can contaminate the primordial signal. We mainly focus on the NG generated from the post inflationary evolution of the CMB anisotropies at second order in perturbation theory at large and small angular scales, such as the ones generated at the recombination epoch. We show how to derive the equations to study the second-order CMB anisotropies and provide analytical computations to evaluate their contamination to primordial NG (complemented with numerical examples). We also offer a brief summary of other secondary effects. This paper requires basic knowledge of the theory of cosmological perturbations at the linear level.

scholarly journals Non Gaussian Minkowski functionals and extrema counts for CMB maps

2014 ◽  
Vol 11 (S308) ◽  
pp. 61-66 ◽  
Author(s):  
Dmitri Pogosyan ◽  
Sandrine Codis ◽  
Christophe Pichon
Keyword(s):  
Cosmic Microwave Background ◽  
Orthogonal Polynomials ◽  
Gaussian Fields ◽  
Spherical Space ◽  
Matter Distribution ◽  
Microwave Background ◽  
Minkowski Functionals ◽  
Second Derivatives ◽  
Non Gaussian ◽  
The Universe

AbstractIn 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.

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