Kolmogorov cosmic microwave background sky

Abstract

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.

To the center of cold spot withPlanck

“…Owing to the hyperbolicity of null geodesics the degree of randomness towards the walls of a void has to be higher than in its inner region (Gurzadyan & Kocharyan 2009a). This property of the cold spot has already been noticed in the WMAP data (Gurzadyan et al 2009), and as several other sky regions with similar properties have been identified. The randomness of the CMB signal has been studied (Gurzadyan & Kocharyan 2008) using the Kolmogorov stochasticity parameter (Kolmogorov 1933;Arnold 2008Arnold , 2009a, which enables determining the degree of randomness in the given sequence of real numbers.…”

“…In the applications to CMB in view of its Gaussian feature, the Gaussian CDF was used for analyzing of the temperature sequences. The obtained Kolmogorov CMB maps (K-maps) for WMAP data readily reveal, for example, the Galactic disk and point sources (galaxies, quasars) that have different randomness (correlation) properties than the cosmological signal (Gurzadyan et al 2009), thus justifying the efficiency and predictive power of the approach.…”

“…underdense regions, with the increase in randomness toward their walls (Gurzadyan et al 2009). Also, a sample of regions has been revealed in the CMB sky, with similar behavior, although less outlined, of the function Φ vs. the radius.…”

Application of the Kolmogorov-Smirnov test to CMB data: Is the universe really weakly random?

“…In this case, the whole sky fails the test: The CMB-dominated areas are biased low, while the galaxy is biased high. This map is similar to the map in Gurzadyan et al (2009), which is also too low outside the galaxy, and too high inside, which is, again, consistent with Gurzadyan et al applying the K-S test directly to the raw samples.…”

“…While Gurzadyan et al's Kolmogorov statistics are biased by not taking the correlations into account, the approach of making sky maps of K-S test results introduced in Gurzadyan et al (2009) is still an interesting way to search for regions of the sky that do not follow the expected distribution. Making an unbiased Kolmogorov map straightforwardly follows the procedure in Sect.…”