Related papers: Pad\'e Approximant and Minimax Rational Approximat…
We propose a novel approach for parameterizing the luminosity distance, based on the use of rational "Pad\'e" approximations. This new technique extends standard Taylor treatments, overcoming possible convergence issues at high redshifts…
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…
As is well known, in mathematics, any function could be approximated by the Pad\'e approximant. The Pad\'e approximant is the best approximation of a function by a rational function of given order. In fact, the Pad\'e approximant often…
Cosmography is used in cosmological data processing in order to constrain the kinematics of the universe in a model-independent way, providing an objective means to evaluate the agreement of a model with observations. In this paper, we…
The cosmography known as the Pad\'{e} polynomials has been widely used in the reconstruction of luminosity distance, and the orders of Pad\'{e} polynomials influence the reconstructed result derived from Pad\'{e} approximation. In this…
The concordance (LambdaCDM) model reproduces the main current cosmological observations assuming the validity of general relativity at all scales and epochs, the presence of cold dark matter, and of a cosmological constant, equivalent to a…
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…
A new analytical solution for the luminosity distance in flat $\Lambda$CDM cosmology is derived in terms of elliptical integrals of first kind with real argument. The consequent derivation of the distance modulus allows evaluating 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)…
Cosmography becomes non-predictive when cosmic data span beyond the red shift limit $z\simeq1 $. This leads to a \emph{strong convergence issue} that jeopardizes its viability. In this work, we critically compare the two main solutions of…
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…
Recently, cosmography emerged as a valuable tool to effectively describe the vast amount of astrophysical observations without relying on a specific cosmological model. Its model-independent nature ensures a faithful representation of data,…
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…
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…
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…
The use of Type~Ia SNe has thus far produced the most reliable measurement of the expansion history of the Universe, suggesting that $\Lambda$CDM offers the best explanation for the redshift--luminosity distribution observed in these…
We present a new distance determination to the Large and Small Magellanic Clouds using the newly developed red clump stars method (Paczynski and Stanek 1998). This new, single-step, Hipparcos calibrated method seems to be one of the most…
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…
Pad$\acute{e}$ cosmography has been widely used to probe the cosmic evolution and to investigate the nature of dark energy. In this paper, we find that the Pad$\acute{e}$ approximant can describe the cosmic evolution better than the…
We consider high-redshift $f(R)$ cosmography adopting the technique of polynomial reconstruction. In lieu of considering Taylor treatments, which turn out to be non-predictive as soon as $z>1$, we take into account the Pad\'e rational…