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We demonstrate an approach that allows separating two-point correlations created by a Gaussian random field from correlations created by cosmic foregrounds such as polarized dust emission, gravitational lensing and other non-Gaussian signals. The result of traditional approaches should typically be a 'foreground-cleaned' two-dimensional CMB map of the anisotropy or polarization. Our method does not create a clean map, but extracts the part of the two-point correlations, or equivalently the part of the power spectrum, which is due only to the Gaussian component of the observed signal produced by inflation., Comment: 3 pages, 1 figure

We present a detailed test for Gaussianity of Planck polarization data using statistics of unpolarized points on the sky, i.e. such points where the linear polarization vanishes. The algorithm we propose for finding such points is stable and guarantees their 100% detection. Our approach allows us to analyze the data for Gaussianity of the signal at different angular scales and detect areas on the polarization maps with a significant contribution from unremoved non-Gaussian foregrounds. We found very strong deviations from Gaussianity for E and B modes in the observational data both over the entire sky and in some specific regions of the celestial sphere., Comment: 12 pages, 6 figures, submitted to Phys. Rev. D

This paper proposes a new approach to separate the $\mu$ spectral distortions of the cosmic microwave background from foregrounds with poorly defined spectral shapes. The idea is based on finding the optimal response to the observed signal. This response is weakly sensitive to foregrounds with parameters that are within some certain limits of their possible variations and, at the same time, very sensitive to the amplitude of $\mu$ distortion. The algorithm described in this paper is stable, easy to implement, and simultaneously minimizes the response to foregrounds and photon noise., Comment: 9 pages, 4 figures

We consider the process of catastrophic expansion of a spacelike wormhole after a violation of its equilibrium state. The dynamics of deformation of the comoving reference frame is investigated. We show that the deformation has a very specific anisotropic feature. The statement made earlier by other authors, that in the process of expanding the wormhole connecting two universes these universes ultimately unite into one universe, is not correct. We show that the transverse size of the wormhole (its throat) increases and the length of the corridor decreases which does not correspond to the de Sitter model.

We consider the Stokes parameters' frequency spectral distortions arising due to Compton scattering of the anisotropic cosmic microwave background (CMB) radiation, the Sunyaev-Zel' dovich effect (SZ), towards clusters of galaxies. We single out a very special type of such distortions and find simple analytical formulas for them. We show that this kind of distortion has a very distinctive spectral shape and can be separated from other kinds of contaminants. We demonstrate that this effect gives us an opportunity for an independent estimation of the low-multipole angular CMB anisotropies, such as the dipole, the quadrupole, and the octupole. We also show that, using distorted signals from nearby and distant clusters, one can distinguish between the Sachs-Wolfe and the integrated Sachs-Wolfe effects. The detection of such distortions can be feasible with high-angular resolution and high-sensitivity space missions, such as the upcoming Millimetron Space Observatory experiment.

We consider the effect of the cosmic microwave background (CMB) frequency spectral distortions arising due to the Compton scattering of the anisotropic radiation on Sunyaev-Zel'dovich (SZ) clusters. We derive the correction to the thermal SZ effect due to the presence of multipoles with $\ell=1,2,3$ in the anisotropy of the CMB radiation. We show that this effect gives us an opportunity for an independent evaluation of the CMB dipole, quadrupole and octupole angular anisotropy in our location using distorted signal from the nearby galaxy clusters and to distinguish between the Sachs-Wolfe (SW) and the Integrated Sachs-Wolfe (ISW) effects by combining such signals from distant and nearby clusters. The future space mission 'Millimetron' will have unprecedented sensitivity, which will make it possible to observe the spectral distortion we are considering., Comment: 8 pages, 8 figures, accepted in Phys.Rev.D

In the framework of the Theory of General Relativity, models of stars with an unusual equation of state $\rho c^2<0$, $P>0$ where $\rho$ is the mass density and $P$ is the pressure, are constructed. These objects create outside themselves the forces of gravitational repulsion. The equilibrium of such stars is ensured by a non-standard balance of forces. Negative mass density, acting gravitationally on itself, creates an acceleration of the negative mass, directed from the center. Therefore in the absence of pressure such an object tends to expand. At the same time, the positive pressure, which falls just like in ordinary stars from the center to the surface, creates a force directed from the center. This force acts on the negative mass density, which causes acceleration directed the opposite of the acting force, that is to the center of the star. This acceleration balances the gravitational repulsion produced by the negative mass. Thus, in our models gravity and pressure change roles: the negative mass tends to create a gravitational repulsion, while the gradient of the pressure acting on the negative mass tends to compress the star. In this paper, we construct several models of such a star with various equations of state., Comment: 6 pages, 4 figures

In this paper we construct a precise mathematical model of the Multiverse, consisted of the universes, that are connected with each other by dynamical wormholes. We consider spherically symmetric free of matter wormholes. At the same time separate universes in this model are not necessary spherically symmetric and can significantly differ from one another. We also analyze a possibility of the information exchange between different universes., Comment: 14 pages, 2 figures

The stability of one type of the static Ellis-Bronnikov-Morris-Thorne wormholes is considered. These wormholes filled with radial magnetic field and phantom dust with a negative energy density., Comment: 6 pages

We report the release of the Gauss--Legendre Sky Pixelization (GLESP) software package version 1.0. In this report we present the main features and functions for processing and manipulation of sky signals. Features for CMB polarization is underway and to be incorporated in a future release. Interested readers can visit http://www.glesp.nbi.dk (www.glesp.nbi.dk) and register for receiving the package.

The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a chi^2 that is large at the 95% level for all scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 sigma. On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data., Comment: 17 pages, 10 figures, accepted for publication in ApJ

A new scheme of sky pixelization is developed for CMB maps. The scheme is based on the Gauss--Legendre polynomials zeros and allows one to create strict orthogonal expansion of the map. A corresponding code has been implemented and comparison with other methods has been done., Comment: 8 pages, 8 figures. Int. J. Mod. Phys. D accepted. For the GLESP software package v1.0 see http://www.glesp.nbi.dk/ (www.glesp.nbi.dk)

We present a new method to extract the beam shape incorporated in the pixelized map of CMB experiments. This method is based on the interplay of the amplitudes and phases of the signal and instrumental noise. By adding controlled white noise onto the map, the phases are perturbed in such a way that the beam shape manifests itself through the mean-squared value of the difference between original and perturbed phases. This method is useful in extracting preliminary antenna beam shape without time-consuming spherical harmonic computations., Comment: 8 pages, 5 figures, submitted to Astronomy & Astrophysics

Analysis of the singularities of the polarization field of CMB, where polarization is equal to zero, is presented. It is found that the classification of the singular points differs from the usual three types known in the ordinary differential equations. The new statistical properties of polarization field are discussed, and new methods to detect the presence of primordial tensor perturbations are indicated., Comment: 7 pages, 1 figures

The distribution of the polarization of the Cosmic Microwave Background (CMB) in the sky is determined by the hypothesis of random Gaussian distribution of the primordial density perturbations. This hypotheses is well motivated by the inflationary cosmology. Therefore, the test of consistency of the statistical properties of the CMB polarization field with the Gaussianity of primordial density fluctuations is a realistic way to study the nature of primordial inhomogeneities in the Universe. This paper contains the theoretical predictions of the general statistical properties of the CMB polarization field. All results obtained under assumption of the Gaussian nature of the signal. We pay the special attention to the following two problems. First, the classification and statistics of the singular points of the polarization field where polarization is equal to zero. Second, the topology of contours of the value of the degree of polarization. We have investigated the percolation properties for the zones of ``strong'' and ``weak'' polarization. We also have calculated Minkowski functionals for the CMB polarization field. All results are analytical., Comment: Latex, 22 pages, including 5 figures

In this paper we develop the theory of clusterization of peaks in a Gaussian random field. We have obtained new mathematical results from this theory and the theory of percolation and have proposed a topological method of analysis of sky maps based on these results. We have simulated $10^o\times10^o$ sky maps of the cosmic microwave background anisotropy expected from different cosmological models with $0.5^o-1^o$ resolution in order to demonstrate how this method can be used for detection of non-Gaussian noise in the maps and detection of the Doppler-peak in the spectrum of perturbation of $\gD T/T$., Comment: 34 pages, 12 postscript figures are available upon request from henning@astro.ku.dk