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.

The ellipticity of the anisotropy spots of the Cosmic Microwave Background measured by the Wilkinson Microwave Anisotropy Probe (WMAP) has been studied. We find an average ellipticity of about 2, confirming with a far larger statistics similar results found first for the COBE-DMR CMB maps, and then for the BOOMERanG CMB maps. There are no preferred directions for the obliquity of the anisotropy spots. The average ellipticity is independent of temperature threshold and is present on scales both smaller and larger than the horizon at the last scattering. The measured ellipticity characteristics are consistent with being the effect of geodesics mixing occurring in an hyperbolic Universe, and can mark the emergence of CMB ellipticity as a new observable constant describing the Universe. There is no way of simulating this effect. Therefore we cannot exclude that the observed behavior of the measured ellipticity can result from a trivial topology in the popular flat Λ-CDM model, or from a non-trivial topology.

The possibility of anisotropies in the speed of light relative to the limiting speed of electrons is considered. The absence of sidereal variations in the energy of Compton-edge photons at the European Synchrotron Radiation Facility's GRAAL facility constrains such anisotropies representing the first nonthreshold collision-kinematics study of Lorentz violation. When interpreted within the minimal standard-model extension, this result yields the two-sided limit of 1.6×10(-14) at 95% confidence level on a combination of the parity-violating photon and electron coefficients (κ(o+))(YZ), (κ(o+))(ZX), c(TX), and c(TY). This new constraint provides an improvement over previous bounds by 1 order of magnitude.

This paper is a follow-up of a previous paper about the M82 galaxy and its halo based on Planck observations. As in the case of M82, so also for the M81 galaxy a substantial North-South and East-West temperature asymmetry is found, extending up to galactocentric distances of about 1.5 0 . The temperature asymmetry is almost frequency independent and can be interpreted as a Doppler-induced effect related to the M81 halo rotation and/or triggered by the gravitational interaction of the galaxies within the M81 Group. Along with the analogous study of several nearby edge-on spiral galaxies, the CMB temperature asymmetry method thus is shown to act as a direct tool to map the galactic haloes and/or the intergalactic bridges, invisible in other bands or by other methods.