Numerical Strategies of Computing the Luminosity Distance

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 replace numerical quadratures. The second method, using a modified version of Hermite interpolation, is less accurate but involves only basic numerical operations and can be easily implemented. We compare our methods with other numerical approximation schemes and explore their respective features and limitations. Possible extensions of these methods to other cosmological models are also discussed.Comment: 4 pages, 2 figures. v2: A minor error in the last equation has been corrected (conclusions are not affected). v3: Accepted by MNRA

An improved method to test the Distance--Duality relation

Many researchers have performed cosmological-model-independent tests for the distance duality (DD) relation. Theoretical work has been conducted based on the results of these tests. However, we find that almost all of these tests were perhaps not cosmological-model-independent after all, because the distance moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent on a given cosmological model and Hubble constant. In this Letter, we overcome these defects and by creating a new cosmological-model-independent test for the DD relation. We use the original data from the Union2 SNe Ia compilation and the angular diameter distances from two galaxy cluster samples compiled by De Filippis et al. and Bonamente et al. to test the DD relation. Our results suggest that the DD relation is compatible with observations, and the spherical model is slightly better than the elliptical model at describing the intrinsic shape of galaxy clusters if the DD relation is valid. However, these results are different from those of previous work.Comment: 5 pages, 2 figures, published on ApJ

Direct reconstruction of dynamical dark energy from observational Hubble parameter data

Reconstructing the evolution history of the dark energy equation of state parameter $w(z)$ directly from observational data is highly valuable in cosmology, since it contains substantial clues in understanding the nature of the accelerated expansion of the Universe. Many works have focused on reconstructing $w(z)$ using Type Ia supernova data, however, only a few studies pay attention to Hubble parameter data. In the present work, we explore the merit of Hubble parameter data and make an attempt to reconstruct $w(z)$ from them through the principle component analysis approach. We find that current Hubble parameter data perform well in reconstructing $w(z)$; though, when compared to supernova data, the data are scant and their quality is worse. Both $\Lambda$CDM and evolving $w(z)$ models can be constrained within $10\%$ at redshifts $z \lesssim 1.5$ and even $5\%$ at redshifts 0.1 $\lesssim$ z $\lesssim$ 1 by using simulated $H(z)$ data of observational quality.Comment: 25 pages, 11 figure