Related papers: An analytical approximation of the luminosity dist…
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 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…
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…
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 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 most recent cosmological observations indicate that the present universe is flat and vacuum dominated. In such a universe, the distance measurements are always difficult and involve numerical computations. 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…
The distance-redshift relation plays an important role in cosmology. In the standard approach to cosmology it is assumed that this relation is the same as in the homogeneous universe. As the real universe is not homogeneous there are…
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…
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 derive and test an approximation for the angular power spectrum of galaxy number counts in the flat sky limit. The standard density and redshift space distortion (RSD) terms in the resulting approximation are distinct to the Limber…
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 present a derivation of the cosmological distance-redshift relation up to second order in perturbation theory. In addition, we find the observed redshift and the lensing magnification to second order. We do not require that the density…
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…
We present the correlation function of the luminosity distances in a flat $\Lambda$CDM universe. Decomposing the luminosity distance fluctuation into the velocity, the gravitational potential, and the lensing contributions, we study their…
We show that the usual relation between redshift and angular-diameter distance can be obtained by considering light from a source to be gravitationally lensed by material that lies in the telescope beam as it passes from source to observer…
The next generation of telescopes will usher in an era of precision cosmology, capable of determining the cosmological model to beyond the percent level. For this to be effective, the theoretical model must be understood to at least the…
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 apparent properties of distant objects encode information about the way the light they emit propagates to an observer, and therefore about the curvature of the underlying spacetime. Measuring the relationship between the redshift $z$…
We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the…