Related papers: A new analytical solution for the distance modulus…
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…
Accurate and efficient methods to evaluate cosmological distances are an important tool in modern precision cosmology. In a flat $\Lambda$CDM cosmology, the luminosity distance can be expressed in terms of elliptic integrals. We derive an…
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…
Cosmological observations indicate that our universe is flat and dark energy (DE) dominated at present. The luminosity distance plays an important role in the investigation of the evolution and structure of the universe. Nevertheless, the…
The tensions between the values of Hubble constant obtained from the early and the late Universe data pose a significant challenge to modern cosmology. Possible modifications of the flat homogeneous isotropic cosmological {\Lambda}CDM model…
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 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…
The distance modulus of the Large Magellanic Cloud (LMC) is the first step on the determination of the cosmic distance scale. In this paper it is obtained from a new calibration of the classical Cepheid Period-Luminosity (PL) relation. Our…
We show that a combined analysis of CMB anisotropy power spectra obtained by the Planck satellite and luminosity distance data simultaneously excludes a flat universe and a cosmological constant at $99 \%$ CL. These results hold separately…
The homogeneous, isotropic, and flat $\Lambda$CDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special…
We present a determination of the Hubble constant from the joint, free-form analysis of 8 strongly, quadruply lensing systems. In the concordance cosmology, we find $H_0 = 71.8^{+3.9}_{-3.3}\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$…
We review the distance modulus in twelve different cosmologies: the $\Lambda$CDM model, the wCDM model, the Cardassian model, the flat case, the $\phi$CDM cosmology, the Einstein--De Sitter model, the modified Einstein--De Sitter model, 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)…
It is shown that the Hubble constant can be derived from the standard luminosity function of galaxies as well as from a new luminosity function as deduced from the mass-luminosity relationship for galaxies. An analytical expression for the…
The most recent Hubble constant ($H_0)$ estimates from local methods (z << 1), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshifts $H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$ confidence…
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…
By the use of homotopy perturbation method-Pad\'e (HPM-Pad\'e) technique, a new analytical approximation of luminosity distance in the flat universe is proposed, which has the advantage of significant improvement for accuracy in…
For 100 years since galaxies were found to be flying apart from each other, astronomers have been trying to determine how fast. The expansion, characterized by the Hubble constant, H0, is confused locally by peculiar velocities caused by…
The LM method, designed to exploit the Hipparcos data to obtain luminosity calibrations, is applied to derive luminosity calibrations for RR Lyrae and classical Cepheids. From these calibrations the distance to the Large Magellanic Cloud…
The luminosity distance in the standard cosmology as given by $\Lambda$CDM and consequently the distance modulus for supernovae can be defined by the Pad\'e approximant. A comparison with a known analytical solution shows that the Pad\'e…