Related papers: Note on the luminosity distance
The luminosity-angular distance relation for an expanding universe is given by $D_L=D_A(1+z)^2$. This relation is commonly proven by geometrical considerations from the source point of view assuming an expanding universe. In this note, the…
We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. We also show the approximate formulae for the so-called Dyer-Roeder distance (empty beam case)…
Recent cosmological observations indicate that the present universe is flat and dark energy dominated. In such a universe, the calculation of the luminosity distance, d_L, involve repeated numerical calculations. In this paper, it is shown…
We present an analytical solution for the luminosity distance in spatially flat cosmology with pressureless matter and the cosmological constant. The complex analytical solution is made of a real part and a negligible imaginary part. The…
We present an analytical approximation formula for the luminosity distance in spatially flat cosmologies with dust and a cosmological constant. Apart from the overall factor, the effect of non-zero cosmological constant in our formula is…
We derive an expression for the luminosity distance as a function of redshift for a flat Robertson-Walker spacetime perturbed by arbitrary scalar perturbations possibly produced by a modified gravity theory with two different scalar…
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…
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…
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 general expression of the angular distance between two point sources as measured by an arbitrary observer is given. The modelling presented here is rigorous, covariant and valid in any space-time. The sources of light may be located at…
Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is…
We present a fitting formula for the luminosity and angular diameter distances in cosmological models with pressureless matter, a cosmological constant and zero spatial curvature. The formula has a relative error of less than 0.4% for…
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…
The Maxwell equations have a fairly simple form. However, finding solutions of Maxwell's equations is an extremely difficult task. Therefore, various simplifying approaches are often used in optics. One such simplifying approach is to use…
We discuss a new formalism for light propagation which can be used within the regime of validity of geometric optics, but with no limitation on the scales of interest: from inside the Galaxy to the ultra-large scales of cosmology. One of…
We study the validity of cosmic distance duality relation between angular diameter and luminosity distances. To test this duality relation we use the latest Union2 Supernovae Type Ia (SNe Ia) data for estimating the luminosity distance. The…
The Lorentzian distance formula, conjectured several years ago by Parfionov and Zapatrin, has been recently proved by the second author. In this work we focus on the derivation of an equivalent expression in terms of the geometry of…
In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift and the proper motion of a luminous source in addition to the variations of redshift and the viewing angle. These…
We propose a new algorithm for computing the luminosity distance in the flat universe with a cosmological constant based on Shchigolev's homotopy perturbation method, where the optimization idea is applied to prevent the arbitrariness of…
We study the continuous limit of the multiple gravitational lensing theory based on the thin lens approximation. Under the approximation, we define a new, light-path dependent angular diameter distance $\tilde{d}$ and show that it satisfies…