Related papers: A general and practical method for calculating cos…
We discuss the problem of how to calculate the distance between two cosmological objects given their redshifts and angular separation on the sky. Although of a fundamental nature, this problem and its solution seem to lack a detailed…
The Universe is not completely homogeneous. Even if it is sufficiently so on large scales, it is very inhomogeneous at small scales, and this has an effect on light propagation, so that the distance as a function of redshift, which in many…
Solving null-geodesic equations, behavior of angular diameter distances is studied in inhomogeneous cosmological models, which are given by performing N-body simulations with the CDM spectrum. The distances depend on the separation angle of…
We study the large-scale inhomogeneity of the Universe based on the averaging procedure of Buchert and Ehlers. The generalized Dyer-Roeder equation for the angular diameter distance of the inhomogeneous Universe is derived and solved for…
Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced…
As the universe expands astronomical observables such as brightness and angular size on the sky change in ways that differ from our simple Cartesian expectation. We show how observed quantities depend on the expansion of space and…
Using the focusing equation, the equation for the cosmological angular diameter distance is derived, based on the ideas of Academician Ya.B. Zel'dovich, namely, that the distribution of matter at small angles is not homogeneous, and the…
We discuss the general and approximate angular diameter distance in the Friedman-Robertson-Walker cosmological models with nonzero cosmological constant. We modify the equation for the angular diameter distance by taking into account the…
We investigate the properties of cosmological distances in locally inhomogeneous universes with pressureless matter and dark energy (quintessence), with constant equation of state. We give exact solutions for angular diameter distances in…
The interpretation of cosmological observations relies on a notion of an average Universe, which is usually considered as the homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) model. However, inhomogeneities may…
We investigate the cosmological test recently proposed by B. Fort, Y. Mellier and M. Dantel-Fort (FMD), where the observed location of the critical line in gravitational lensing is used to determine the cosmological parameters, $\Omega$ and…
The standard cosmological parallax--distance formula, as found in the literature, including text-books and reference books on cosmology, requires a correction. This correction stems from the fact that in the standard text-book derivation it…
Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…
The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case…
This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various…
Accurate and precise astronomical distance determinations are crucial for derivations of, among others, the masses and luminosities of a large variety of distant objects. Astronomical distance determination has traditionally relied on the…
We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat {\Lambda}CDM universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can…
We calculate the low red-shift Taylor expansion for the luminosity distance for an observer at the center of a spherically symmetric matter inhomogeneity with a non vanishing cosmological constant. We then test the accuracy of the formulas…
We present our development of Zeldovich's ideas for the measurement of the cosmological angular diameter distance (ADD) in the Friedmann Universe. We derive the general differential equation for the ADD measurement which is valid for an…
We present a brief history of the construction of models of the universe, followed by calculations of quantitative characteristics of basic geometric and kinematic properties of the Standard Cosmological Model ($\Lambda$CDM). Using the…