Comparison of cosmological models using standard rulers and candles

In this paper, we used standard rulers and standard candles(separately and jointly) to explore five popular dark energy models under the assumption of the spatial flatness of the Universe. As standard rulers, we used a data set comprised of 118 galactic scale strong lensing systems(individual standard rulers if properly calibrated for the mass density profile) combined with BAO diagnostics(statistical standard ruler). Type Ia supernovae served as standard candles. Unlike most previous statistical studies involving strong lensing systems, we relaxed the assumption of a singular isothermal sphere(SIS) in favor of its generalization: the power-law mass density profile. Therefore, along with cosmological model parameters,we fitted the power law index and its first derivative with respect to the redshift(thus allowing for mass density profile evolution). It turned out that the best fitted γ parameters are in agreement with each other,irrespective of the cosmological model considered. This demonstrates that galactic strong lensing systems may provide a complementary probe to test the properties of dark energy. The fits for cosmological model parameters which we obtained are in agreement with alternative studies performed by other researchers.Because standard rulers and standard candles have different parameter degeneracies, a combination of standard rulers and standard candles gives much more restrictive results for cosmological parameters. Finally,we attempted an analysis based on model selection using information theoretic criteria(AIC and BIC). Our results support the claim that the cosmological constant model is still best and there is no(at least statistical)reason to prefer any other more complex model.