/ 99 02 13 3 v 1 9 F eb 1 99 9 Kolmogorov Complexity , Cosmic Microwave

The information theory approach is suggested to the Cosmic Microwave Background (CMB) problem for negatively curved homogeneous and isotropic Universe. Namely, the Kolmogorov complexity of anisotropy of spots in CMB sky maps is proposed as a new descriptor for revealing crucial cosmological information, particularly on the curvature of the Universe. Such profound descriptor can be especially valuable while analyzing the data of forthcoming space and ground based experiments MAP, Planck surveyor, CAT, etc. PACS 98.80-Cosmology PACS 98 70V-Background radiation The Cosmic Microwave Background radiation data and particularly the sky maps are an essential source of cosmological information. Various de-scriptors have been proposed to extract that information, including the hot spot number density, genus, correlation function of local maxima, Euler-Poincare characteristic, etc. (for review see [1]). Most of these descriptors have been already applied for the analysis of COBE sky maps [2]. However , in view of forthcoming new generation high precision experiments, the importance of involving of more refined descriptors, is evident. In the present paper we turn attention to a new descriptor, namely to the Kolmogorov complexity of the CMB anisotropy spots, which can carry important information on the geometry of the Universe. The idea is based on the effect of geodesic mixing [3] occurring in Friedmann-Robertson-Walker (FRW) Universe with negative curvature. Several observable consequences of this effect for CMB properties have been predicted [4],[5], including: (a) decrease of the amplitude of the anisotropy after the last scattering epoch, (b) flattening of the angular autocorrelation function, (c) distortion of the sky maps. Particularly, the distortion of anisotropy spots is a result of strong sta