The Effects of Inhomogeneities on Evaluating the mass parameter Ωm\Omega_m and the cosmological constant Λ\Lambda

Analytic expressions for distance-redshift relations which have been corrected for the effects of inhomogeneities in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) mass density are given in terms of Heun functions and are used to illustrate the significance of inhomogeneities on a determination of the mass parameter $\Omega_m$ and the cosmological constant $\Lambda$. The values of these parameters inferred from a given set of observations depend on the fractional amount of matter in inhomogeneities and can significantly differ from those obtained by using the standard magnitude-redshift ($m$-$z$) result for pure dust FLRW models. As an example a determination of $\Omega_m$ made by applying the homogeneous distance-redshift relation to SN 1997ap at $z=0.83$ could be as much as 50% lower than its true value.Comment: 39 pages including 8 figures and captions. To appear in ApJ 507 (Nov. 1998

Dephosphorization of Manganese Ore Raw Materials

The dephosphorization of manganese ores and concentrates in a reducing atmosphere is thermodynamically analyzed. It is shown that phosphorus can completely pass to a gas phase in a closed reaction system in a wide temperature range (1273–2073 K) at the amounts of a reducing gas (CO) that exceed the stoichiometric minimum required for reduction reactions. The gaseous products of reduction is found to contain phosphorus in the form of mainly polyatomic “heavy” molecular oxides, which can decrease the real effect of dephosphorization as compared to that obtained by equilibrium calculations because of kinetic factors. A thermodynamic simulation of a flow reaction system shows that almost complete transition of phosphorus to light gaseous substances (PO, P2) is thermodynamically possible at the temperatures that are close to the technological operation temperatures. This transition is provided by the ratio of the rate of formation of volatile phosphorus-containing substances to the rate of their removal from reaction regions. Keywords: manganese ores, manganese concentrates, phosphorus, carbon monoxide, reductio

Observational constraints on inhomogeneous cosmological models without dark energy

It has been proposed that the observed dark energy can be explained away by the effect of large-scale nonlinear inhomogeneities. In the present paper we discuss how observations constrain cosmological models featuring large voids. We start by considering Copernican models, in which the observer is not occupying a special position and homogeneity is preserved on a very large scale. We show how these models, at least in their current realizations, are constrained to give small, but perhaps not negligible in certain contexts, corrections to the cosmological observables. We then examine non-Copernican models, in which the observer is close to the center of a very large void. These models can give large corrections to the observables which mimic an accelerated FLRW model. We carefully discuss the main observables and tests able to exclude them.Comment: 27 pages, 7 figures; invited contribution to CQG special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology". Replaced to match the improved version accepted for publication. Appendix B and references adde

The Effect of Large-Scale Inhomogeneities on the Luminosity Distance

We study the form of the luminosity distance as a function of redshift in the presence of large scale inhomogeneities, with sizes of order 10 Mpc or larger. We approximate the Universe through the Swiss-cheese model, with each spherical region described by the Tolman-Bondi metric. We study the propagation of light beams in this background, assuming that the locations of the source and the observer are random. We derive the optical equations for the evolution of the beam area and shear. Through their integration we determine the configurations that can lead to an increase of the luminosity distance relative to the homogeneous cosmology. We find that this can be achieved if the Universe is composed of spherical void-like regions, with matter concentrated near their surface. For inhomogeneities consistent with the observed large scale structure, the relative increase of the luminosity distance is of the order of a few percent at redshifts near 1, and falls short of explaining the substantial increase required by the supernova data. On the other hand, the effect we describe is important for the correct determination of the energy content of the Universe from observations.Comment: 27 pages, 5 figures Revised version. References added. Conclusions clarifie