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The emission in the hyperfine structure 21 cm line of atomic hydrogen arising in the halos with masses $\sim10^6-10^{10}$ M$_\odot$ from the Dark Ages in the models with Warm Dark Matter (WDM) is analysed. The halos are assumed to be formed from Gaussian density peaks of cosmological density perturbations at $10\lesssim z\lesssim50$. Semi-analytical modelling of the formation of individual spherical halos in multi-component models shows that gas in them has the kinetic temperature in the range of $60-800$ K under adiabatic compression of the collapsing halo, and the temperature of each halo depends on the time of virialization. It is shown that inelastic collisions between neutral hydrogen atoms are the dominant excitation mechanism for hyperfine structure levels, which pulls the spin temperature closer to the kinetic temperature. The brightness temperature of individual halos is in the range of 1-10 K, depending on the mass of the halo and its virialization redshift, and increasing as these two increase. The apparent angular radii of such halos are in the range 0.06-1.2 arcseconds, their surface number density decreasing exponentially from a few per arcmin$^2$ for the lowest mass and redshift to nearly zero for higher values. Assuming a 1 MHz observation bandwidth the surface number density of the halo at various redshifts is evaluated as well as beam-averaged differential antenna temperatures and fluxes of hydrogen emission from halos of different masses. The beam-averaged signal strongly depends on the cut-off scale in the mass function of dark ages halos that may be caused by free-streaming of WDM particles. The finding is compared with the upper limits on the amplitude of the power spectrum of the hydrogen 21-cm line fluctuations derived from the recent observation data obtained with MWA and LOFAR., Comment: 18 pages, 10 figures, 7 tables; accepted for publication in Physics of the Dark Universe

We analyse the thermal emission and resonant scattering of CMB radiation from the dark ages halos in the rotational lines of the helium hydride ion (HeH$^{+}$), one of the first chemical compounds in the Universe. Evaluating the optical depth, thermal and resonant brightness temperatures and spectral fluxes of dark ages halos is based on computing the cross-sections and rate coefficients of excitation/de-excitation of the lowest five rotational states of HeH$^{+}$ by inelastic collisions with atomic hydrogen. It was shown that in the Dark Ages the collisional excitation/de-excitation by atoms of neutral hydrogen and electrons are competitive, whereas in the denser regions, e.g., in the halos, the contribution of collisions with atomic hydrogen is dominant. We demonstrate the peak-like time-dependence of halo luminosities in HeH$^{+}$ lines., Comment: 13 pages, 9 figures, 9 tables; accepted for publication in Phys.Rev.D

The emission from dark ages halos in the lines of transitions between lowest rotational levels of hydrogen and hydrogen deuteride molecules is analyzed. It is assumed molecules to be excited by CMB and collisions with hydrogen atoms. The physical parameters of halos and number density of molecules are precalculated in assumption that halos are homogeneous top-hat spheres formed from the cosmological density perturbations in the four-component Universe with post-Planck cosmological parameters. The differential brightness temperatures and differential spectral fluxes in the rotational lines of H$_2$-HD molecules are computed for two phenomena: thermal luminescence and resonant scattering of CMB radiation. The results show that expected maximal values of differential brightness temperature of warm halos ($T_K\sim$200-800 K) are at the level of nanokelvins, are comparable for both phenomena, and are below sensitivity of modern sub-millimeter radio telescopes. For hot halos ($T_K\sim$2000-5000 K) the thermal emission of H2-ortho molecules dominates and the differential brightness temperatures are predicted to be of a few microkelvins at the frequencies 300-600 GHz, that could be detectable with telescopes of a new generation., Comment: 18 pages, 9 figures, 16 tables; accepted for publication in ApJ; in the revised version the discussion about impact of new coefficients of collision excitation H2-H on the brightness temperature as well as the comparison with results of other authors are added

It is considered a model of compact Riemann surface in genus two, represented geometrically by two-parametric hyperbolic octagon with an order four automorphism and described algebraically by the corresponding Fuchsian group. Introducing the Fenchel--Nielsen variables, we compute the Weil--Petersson (WP) symplectic two-form for parameter space and analyze the closed isoperimetric orbits of octagons. WP-Area in parameter space and the canonical action--angle variables for the orbits are found. Exploiting the ideas from the loop quantum gravity, we generate relativistic kinematics by the Lorentz boost and quantize WP-area. We treat the evolution in terms of global variables within the "big bounce" concept., Comment: 18 pages, 7 figures

The distribution of dark energy density in the vicinity of compact static objects is analyzed. Dark energy is assumed to be in the form of a scalar field with three parameters: the background density, the equation of state parameter and the effective sound speed. Compact object is assumed to be a homogeneous spherical object of constant radius. We use the solutions of the hydrodynamical equations for dark energy in the gravitational fields of such objects for cases of static distribution of dark energy in the vicinity of star and stationary accretion onto black hole in order to analyze the possibility of constraining of the parameters of dark energy from astrophysical data. We show that dependence of density of dark energy in the vicinity of such object on the effective sound speed, background density and equation of state parameter of dark energy makes it possible to try such tests. Here we exploit the accuracy of determination of masses of Sun and black hole in the center of Milky Way to obtain the lower limit on the effective sound speed of dark energy., Comment: 5 pages, 2 figures; WDS'14 Proceedings of Contributed Papers

We study the dynamical properties and space distribution of dark energy in the weak and strong gravitational fields caused by inhomogeneities of matter in the static world of galaxies and clusters. We show that the dark energy in the weak gravitational fields of matter density perturbations can condense or dilute, but amplitudes of its perturbations remain very small on all scales. We illustrate also how the "accretion" of the phantom dark energy onto the matter overdensity forms the dark energy underdensity. We analyze the behavior of dark energy in the gravitational fields of stars and black holes with the Schwarzschild metric. It is shown that, in the case of stars, the static solution of the differential equations for energy-momentum conservation exists and describes the distribution of density of dark energy inside and outside of a star. We have found that for stars and galaxies its value differs slightly from the average and is a bit higher for the quintessential scalar field as dark energy and a bit lower for the phantom one. The difference grows with the decrease of the effective sound speed of dark energy and is large in the neighborhood of neutron stars. We obtain and analyze also the solutions of equations that describe the stationary accretion of the dark energy as a test component onto the Schwarzschild black hole. It is shown that the rate of change of mass of the dark energy is positive in the case of quintessential dark energy and is negative in the case of the phantom one., Comment: 13 pages, 4 figures, 1 table; v2: text corrected and supplemented; v3: corrected to the version accepted for publication in Phys. Rev. D

The Workshop on results of the Project Kosmomikrofizyka-2 (Astroparticle Physics) of the National Academy of Sciences (NAS) of Ukraine "Astrophysical and cosmological problems of invisible mass and dark energy in the Universe" was held on November 21-22, 2012 in the Institute for Nuclear Research, Kyiv, Ukraine (http://lpd.kinr.kiev.ua/kmf12). This Project was carried out during three years (2010-2012) by scientists from various universities and institutes of the National Academy of Sciences of Ukraine; it was a logical continuation of the previous scientific program of the NAS of Ukraine "Researches of structure and composition of the Universe, hidden mass and dark energy (Kosmomikrofizyka)" in 2007-2009. These programs were devoted to theoretical and experimental investigations in astronomy, astrophysics, cosmology, physics of atomic nuclei and particle physics, which are related with the problems of dark matter and dark energy in the Universe., Comment: Proceedings of the Workshop on results of the Project Kosmomikrofizyka-2 (Astroparticle Physics) of the National Academy of Sciences of Ukraine, November 21-22, 2012, Institute for Nuclear Research, Kyiv, Ukraine. 94 pages, 29 figures, 5 tables (in English, Ukrainian, Russian)

We analyse the redshift dependence of space number density of quasars assuming that they are the short-lived active stages of the massive galaxies and arise immediately after the collapse of homogeneous central part of protogalaxy clouds. Obtained dependence fits the observational data ChaMP+CDF+ROSAT (Silverman et al. 2005) very well for protogalaxy clouds of mass $M\approx 8\cdot 10^{11}$ $h^{-1}M_{\odot}$ and ellipticity $e<0.4$. The lifetime of bright X-ray AGNs or QSOs with $L_X>10^{44.5}$ erg$\cdot s^{-1}$ in the range of energies $0.3-8$ keV is $\tau_{QSO}\sim 6\cdot10^6$ years when the mass of supermassive black hole is $M_{SMBH}\sim 10^{9}$ $M_{\odot}$ and the values of other quasar parameters are reasonable. The analysis and all calculations were carried out in the framework of $\Lambda$CDM-model with parameters determined from 5-years WMAP, SNIa and large scale structure data (Komatsu et al. 2009). It is concluded, that the halo model of galaxy formation in the $\Lambda$CDM cosmological model matches well observational data on AGNs and QSOs number density coming from current optical and X-ray surveys., Comment: 8 pages, 1 figure; published in J. Phys. Studies, v. 14, No. 2, p. 2901-1 (2010); http://www.ktf.franko.lviv.ua/JPS/index_ua.html

The evolution of scalar perturbations is studied for 2-component (non-relativistic matter and dark energy) cosmological models at the linear and non-linear stages. The dark energy is assumed to be the scalar field with either classical or tachyonic Lagrangian and constant equation-of-state parameter w. The fields and potentials were reconstructed for the set of cosmological parameters derived from observations. The comparison of the calculated within these models and experimental large-scale structure characteristics is made. It is shown that for w=const such analysis can't remove the existing degeneracy of the dark energy models., Comment: 15 pages, 5 figures, text corrected, references added, accepted by Kinematics and Physics of Celestial Bodies

The parameters of cosmological model with cold dark matter and cosmological constant (Lambda CDM) have been determined on a basis of three-year cosmic microwave background observations by space mission WMAP, as well as the data on the large-scale structure of the Universe. The data cover scales from 1 up to 10000 Mpc. The best-fit values of LambdaCDM model parameters were found by minimization of chi^2 using the Levenberg-Markquardt approach (Omega_Lambda=0.736+-0.065, Omega_m=0.238+-0.080, Omega_b=0.05+-0.011, h=0.68+- 0.09, sigma_8=0.73+-0.08 and n_s=0.96+-0.015). It is shown that the LambdaCDM model with these values of the parameters agrees well with the angular power spectrum of cosmic microwave background and with power spectra of the density perturbations, estimated from spatial distributions of galaxies, rich galaxy clusters and from statistics of Ly_alpha absorption lines in spectra of distant quasars as well. The accordance of modeled characteristics of the large-scale structure with observable ones was analyzed, and possible reasons of significant discrepancies between some of them were considered., Comment: 12 pages, 6 figures, translation from Ukrainian

The evolution of matter density perturbations in two-component model of the Universe consisting of dark energy (DE) and dust-like matter (M) is considered. We have analyzed it for two kinds of DE with $\omega\ne -1$: a) unperturbed energy density and b) perturbed one (uncoupled with matter). For these cases the linear equations for evolution of the gauge-invariant amplitudes of matter density perturbations are presented. It is shown that in the case of unperturbed energy density of DE the amplitude of matter density perturbations grow slightly faster than in the second case., Comment: 4 pages, 1 figure, submitted to the proceedings of international conference "Astronomy in Ukraine - Past, Present, Future", July 15-17, Kiev, Ukraine

We have analyzed the dependences of the threshold value of amplitude of linear density fluctuation collapsed at the current epoch, $\delta_c$, and its overdensity after virialization, $\Delta_c$, on matter density content, 3D curvature parameter and cosmological constant. Though the range for the threshold values of perturbation amplitude is quite narrow - $1.55\le \delta_c\le 1.75$ in the region of parameters $-0.4\le\Omega_k\le0.4$, $0\le\Omega_{\Lambda}\le 1$, $0.1\le\Omega_m\le 1$, the difference in the concentrations of rich clusters of galaxies (calculated within the Press-Schechter formalism framework) with real and with canonical values of $\delta_c$ reaches, and for some models exceeds, 30%. The range of changes for the overdensity after virialization, $\Delta_c$, is considerably wider for the same region of parameters: $60\le\Delta_c\le180$. It results into difference up to $\sim40$% between the X-ray temperatures of gas, as calculated for these values and for the canonical value of $\Delta_c=178$. Also we have found analytical approximations of the dependences $\delta_c(\Omega_m,\Omega_{\Lambda})$ and $\Delta_c(\Omega_m,\Omega_{\Lambda})$ with their accuracies for above mentioned region of parameters being no worse than 0.2% and 1.7% respectively., Comment: 17 pages, 8 figures, LaTeX (Accepted for publication by Journal of Physical Studies, 2003, No1)