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Astron. Astrophys. 364, 17-25 (2000)

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On non-Gaussianity in the cosmic microwave background

D. Novikov 1,2,3, J. Schmalzing 1,4 and V.F. Mukhanov 1

1 Ludwig-Maximilians-Universität, Theresienstrasse 37, 80333 München, Germany (novikov,jens,mukhanov@theorie.physik.uni-muenchen.de)
2 Astronomy Department, Keble Road, Oxford OX1 3RH, UK
3 Astro-Space Center, P. N. Lebedev Physical Institute, 84/32 Profsoyuznaya st., Moscow, 117810, Russia
4 Teoretisk Astrofysik Center, Juliane Maries Vej 30, 2100 Kobenhavn O, Denmark

Received 8 June 2000 / Accepted 31 August 2000

Abstract

We consider a cosmological model with non-Gaussian initial perturbations, which in principle could be generated in non-standard inflationary scenarios with two or more scalar fields. In particular we focus our attention on the model proposed by Linde & Mukhanov (1997), where perturbations are quadratic in a Gaussian field. These perturbations, if they exist, have to be observable as a non-Gaussian distribution of the CMB signal on the sky. In order to efficiently pick up the non-Gaussian signal in CMB maps of degree resolution, one can use Minkowski Functionals and peak statistics. Our paper contains the theoretical predictions of the properties for Minkowski Functionals and distributions of peaks of the CMB anisotropy in the model with "squared" Gaussian statistics. Likelihood comparison of the four-year COBE DMR data to this non-Gaussian model and the standard Gaussian model does not select any of them as most likely.

We also suggest an efficient algorithm for fast simulation of CMB maps on the whole sky. Using a cylindrical partition of the sphere, we rewrite the spherical harmonics analysis as a Fourier transform in flat space, which makes the problem accessible to numerically advantageous FFT methods.

Key words: methods: numerical – methods: statistical – cosmology: cosmic microwave background – cosmology: observations

Send offprint requests to: D. Novikov

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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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