Probing the statistic in the cosmic microwave background

Kolmogorov's statistic is used for the analysis of properties of perturbations in the Cosmic Microwave Background signal. We obtain the maps of the Kolmogorov stochasticity parameter for W and V band temperature data of WMAP which are differently affected by the Galactic disk radiation and then we model datasets with various statistic of perturbations. The analysis shows that the Kolmogorov's parameter can be an efficient tool for the separation of Cosmic Microwave Background from the contaminating radiations due to their different statistical properties.Comment: 6 pages, 4 figure

A weakly random Universe?

The cosmic microwave background (CMB) radiation is characterized by well-established scales, the 2.7 K temperature of the Planckian spectrum and the $10^{-5}$ amplitude of the temperature anisotropy. These features were instrumental in indicating the hot and equilibrium phases of the early history of the Universe and its large scale isotropy, respectively. We now reveal one more intrinsic scale in CMB properties. We introduce a method developed originally by Kolmogorov, that quantifies a degree of randomness (chaos) in a set of numbers, such as measurements of the CMB temperature in some region. Considering CMB as a composition of random and regular signals, we solve the inverse problem of recovering of their mutual fractions from the temperature sky maps. Deriving the empirical Kolmogorov's function in the Wilkinson Microwave Anisotropy Probe's maps, we obtain the fraction of the random signal to be about 20 per cent, i.e. the cosmological sky is a weakly random one. The paper is dedicated to the memory of Vladimir Arnold (1937-2010).Comment: 4 pages, 3 figs, A & A (Lett) in press; to match the published versio

Degree of randomness: numerical experiments for astrophysical signals

Astrophysical and cosmological signals such as the cosmic microwave background radiation, as observed, typically contain contributions of different components, and their statistical properties can be used to distinguish one from the other. A method developed originally by Kolmogorov is involved for the study of astrophysical signals of randomness of various degrees. Numerical performed experiments based on the universality of Kolmogorov distribution and using a single scaling of the ratio of stochastic to regular components, reveal basic features in the behavior of generated signals also in terms of a critical value for that ratio, thus enable the application of this technique for various observational datasetsComment: 6 pages, 9 figures; Europhys.Letters; to match the published versio

Kolmogorov cosmic microwave background sky

A new map of the sky representing the degree of randomness in the cosmic microwave background (CMB) temperature has been obtained. The map based on estimation of the Kolmogorov stochasticity parameter clearly distinguishes the contribution of the Galactic disk from the CMB and reveals regions of various degrees of randomness that can reflect the properties of inhomogeneities in the Universe. For example, among the high randomness regions is the southern non-Gaussian anomaly, the Cold Spot, with a stratification expected for the voids. Existence of its counterpart, a Northern Cold Spot with almost identical randomness properties among other low-temperature regions is revealed. By its informative power, Kolmogorov's map can be complementary to the CMB temperature and polarization sky maps.Comment: A & A (in press), to match the published version, 4 pages, 5 figs, 2 Table

Detection of X-ray galaxy clusters based on the Kolmogorov method

The detection of clusters of galaxies in large surveys plays an important part in extragalactic astronomy, and particularly in cosmology, since cluster counts can give strong constraints on cosmological parameters. X-ray imaging is in particular a reliable means to discover new clusters, and large X-ray surveys are now available. Considering XMM-Newton data for a sample of 40 Abell clusters, we show that their analysis with a Kolmogorov distribution can provide a distinctive signature for galaxy clusters. The Kolmogorov method is sensitive to the correlations in the cluster X-ray properties and can therefore be used for their identification, thus allowing to search reliably for clusters in a simple way

Large scale plane-mirroring in the cosmic microwave background WMAP5 maps

We continue investigation of the hidden plane-mirror symmetry in the distribution of excursion sets in cosmic microwave background (CMB) temperature anisotropy maps, previously noticed in the three-year data of the Wilkinson microwave anisotropy probe (WMAP), using the WMAP 5 years maps. The symmetry is shown to have higher significance, $\chi^2 < 1.7$, for low multipoles $\ell 3.5$ for $\ell > 10$. The study of the sum and difference maps of temperature inhomogeneity regions, along with simulated maps, confirms its existence. The properties of these mirroring symmetries are compatible with those produced by the Sachs-Wolfe effect in the presence of an anomalously large component of horizon-size density perturbations, independent of one of the spatial coordinates, and/or a slab-like spatial topology of the Universe