Related papers: Computing the luminosity distance via optimal homo…
Local structure can have important effects on luminosity distance observations, which could for example affect the local estimation of the Hubble constant based on low red-shift type Ia supernovae. Using a spherically symmetric exact…
We study the computational complexity of determining the Hausdorff distance of two polytopes given in halfspace- or vertex-presentation in arbitrary dimension. Subsequently, a matching problem is investigated where a convex body is allowed…
Based on the luminosity-distance diagram, we propose a method to quickly estimate the luminosity function for any certain astrophysical objects. Giving the mean distance between any two objects at a given luminosity range, we can find the…
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…
We calculate the systematic inhomogeneity-induced correction to the cosmological constant that one would infer from an analysis of the luminosities and redshifts of Type Ia supernovae, assuming a homogeneous universe. The calculation…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
We introduce two new algebraic invariants, the (co)homological distances between continuous maps, which provide computable lower bounds for the homotopic distance and strictly refine the classical cup-length estimates. We then define the…
The luminosity distance can be used to determine the properties of large scale structure around the observer. To this purpose we develop a new inversion method to map luminosity distance to a LTB metric based on the use of the exact…
In this paper, the homotopy-perturbation method (HPM) is applied to obtain approximate analytical solutions for the gravitational deflection of light in General Relativity near Schwarzschild black hole surrounded by quintessence (Kiselev…
We re-derive a formula relating the areal and luminosity distances, entirely in the framework of the classical Maxwell theory, assuming a geometric-optics type condition.
The Gromov--Hausdorff distance measures the difference in shape between metric spaces and poses a notoriously difficult problem in combinatorial optimization. We introduce its quadratic relaxation over a convex polytope whose solutions…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
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…
The second derivative of the luminosity distance with respect to the redshift is written in terms of the deceleration parameter $q_0$. We point out that the third derivative contains the information regarding the sound speed of cosmic…
We derive luminosity distance equation in Gurzadyan-Xue cosmological models and compared it with available supernovae and radio galaxies data sets. We found that the luminosity distance does not depend explicitly the speed of light and the…
Using numerical ray tracing, the paper studies how the average distance modulus in an inhomogeneous universe differs from its homogeneous counterpart. The averaging is over all directions from a fixed observer not over all possible…
We introduce a novel way of measuring $H_0$ from a combination of independent geometrical datasets, with no need of calibration nor of the choice of a cosmological model. We build on the {\it distance duality relation} which sets the ratio…
The calculation of distances is of fundamental importance in extragalactic astronomy and cosmology. However, no practical implementation for the general case has previously been available. We derive a second-order differential equation for…
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…
Cosmography has been extensively utilized to constrain the kinematic state of the Universe using measured distances. In this work, we propose a new method to reconstruct coupling theories using the first kind of Chebyshev polynomial for two…