Distant foreground and the Planck-derived Hubble constant

It is possible to reduce the discrepancy between the local measurement of the cosmological parameter $H_0$ and the value derived from the $Planck$ measurements of the Cosmic Microwave Background (CMB) by considering contamination of the CMB by emission from some medium around distant extragalactic sources, such as extremely cold coarse-grain dust. Though being distant, such a medium would still be in the foreground with respect to the CMB, and, as any other foreground, it would alter the CMB power spectrum. This could contribute to the dispersion of CMB temperature fluctuations. By generating a few random samples of CMB with different dispersions, we have checked that the increased dispersion leads to a smaller estimated value of $H_0$, the rest of the cosmological model parameters remaining fixed. This might explain the reduced value of the $Planck$-derived parameter $H_0$ with respect to the local measurements. The signature of the distant foreground in the CMB traced by SNe was previously reported by the authors of this paper -- we found a correlation between the SN redshifts, $z_{\rm SN}$, and CMB temperature fluctuations at the SNe locations, $T_{\rm SN}$. Here we have used the slopes of the regression lines $T_{\rm SN}\,/\,z_{\rm SN}$ corresponding to different {\it Planck} wave bands in order to estimate the possible temperature of the distant extragalactic medium, which turns out to be very low, about 5\,K. The most likely ingredient of this medium is coarse-grain ($grey$) dust, which is known to be almost undetectable, except for the effect of dimming remote extragalactic sources.Comment: 5 pages, 4 figures, 1 tabl

The Non-Uniform Distribution of Galaxies from Data of the SDSS DR7 Survey

We have analyzed the spatial distribution of galaxies from the release of the Sloan Digital Sky Survey of galactic redshifts (SDSS DR7), applying the complete correlation function (conditional density), two-point conditional density (cylinder), and radial density methods. Our analysis demonstrates that the conditional density has a power-law form for scales lengths 0.5-30 Mpc/h, with the power-law corresponding to the fractal dimension D = 2.2+-0.2; for scale lengths in excess of 30 Mpc/h, it enters an essentially flat regime, as is expected for a uniform distribution of galaxies. However, in the analysis applying the cylinder method, the power-law character with D = 2.0+-0.3 persists to scale lengths of 70 Mpc/h. The radial density method reveals inhomogeneities in the spatial distribution of galaxies on scales of 200 Mpc/h with a density contrast of two, confirming that translation invariance is violated in the distribution of galaxies to 300 Mpc/h, with the sampling depth of the SDSS galaxies being 600 Mpc/h.Comment: 22 page

Method of analysis of the spatial galaxy distribution at gigaparsec scales. I. Initial principles

Initial principles of a method of analysis of the luminous matter spatial distribution with sizes about thousands Mpc are presented. The method is based on an analysis of the photometric redshift distribution N(z) in the deep fields with large redshift bins \Deltaz=0.1{\div}0.3. Number density fluctuations in the bins are conditioned by the Poisson's noise, the correlated structures and the systematic errors of the photo-z determination. The method includes covering of a sufficiently large region on the sky by a net of the deep multiband surveys with the sell size about 10^{\circ}x10^{\circ} where individual deep fields have angular size about 10'x10' and may be observed at telescopes having diameters 3-10 meters. The distributions of photo-z within each deep field will give information about the radial extension of the super large structures while a comparison of the individual radial distributions of the net of the deep fields will give information on the tangential extension of the super large structures. A necessary element of the method is an analysis of possible distortion effects related to the methodic of the photo-z determination.Comment: 12 page

Finite Arithmetic Axiomatization for the Basis of Hyperrational Non-Standard Analysis

The standard elementary number theory is not a finite axiomatic system due to the presence of the induction axiom scheme. Absence of a finite axiomatic system is not an obstacle for most tasks, but may be considered as imperfect since the induction is strongly associated with the presence of set theory external to the axiomatic system. Also in the case of logic approach to the artificial intelligence problems presence of a finite number of basic axioms and states is important. Axiomatic hyperrational analysis is the axiomatic system of hyperrational number field. The properties of hyperrational numbers and functions allow them to be used to model real numbers and functions of classical elementary mathematical analysis. However hyperrational analysis is based on well-known non-finite hyperarithmetic axiomatics. In the article we present a new finite first-order arithmetic theory designed to be the basis of the axiomatic hyperrational analysis and, as a consequence, mathematical analysis in general as a basis for all mathematical application including AI problems. It is shown that this axiomatics meet the requirements, i.e., it could be used as the basis of an axiomatic hyperrational analysis. The article in effect completes the foundation of axiomatic hyperrational analysis without calling in an arithmetic extension, since in the framework of the presented theory infinite numbers arise without invoking any new constants. The proposed system describes a class of numbers in which infinite numbers exist as natural objects of the theory itself. We also do not appeal to any “enveloping” set theory