Testing The Distance-duality Relation And Applying It In Cosmology

As the astronomical observation technology improving in the past years, we get more precise and more kinds of data. It makes it possible for us to make constraints on universe parameters and test some basic cosmology relations. Firstly, we perform a cosmological model independent test of the cosmic distance-duality relation （CDDR） in terms of the ratio of angular diameter distance （ADD） D = D_A^sl/D_A^s from strong gravitational lensing （SGL） and the ratio of luminosity distance （LD）D^*=D_L^l/D_L^s obtained from the joint of type la supernovae （SNIa） Union2.1 compilation and the latest Gamma-Ray Bursts （GRBs） data,where the superscripts s and 1 correspond to the redshifts z_s and z_l at the source and lens from SGL samples. The purpose of combining GRB data with SNIa compilation is to test CDDR in a wider redshift range. The LD associated with the redshits of the observed ADD, is obtained through two cosmological model-independent methods, namely, method A: binning the SNIa+GRBs data, and method B: reconstructing the function of DL by combining the Crossing Statistic with the smoothing method. We find that CDDR is compatible with the observations at 1σ confidence level for the power law model which is assumed to describe the mass distribution of lensing systems with method B in a wider redshift range.We also reconstructed the cosmic expansion history and the evolving property of dark energy. Many researchers have performed cosmological model independent reconstruction for the cosmic expansion history and the evolving property of dark energy over a given type la supernovae compilation. However, we show that almost all of the reconstructions in which the distance modulus are directly taken from SNe la data were perhaps not cosmological-model-independent. In this paper, in order to overcome this defect, with the help of CDDR, we first calibrate the light-curve fitting parameters in the distance estimation from the original Union2.1 SNe la compilation. Three model-independent methods （nearby method, interpolation method and binning method） are proposed to obtain the data pairs of observational DLand DAalmost at the same redshift. Then, we reestimate the distance modulus for the SNe la with the corrected fitting parameters, and finally implement a cosmological-model-independent reconstruction for the cosmic expansion history and the evolving property of dark energy. We find that our reconstructed results are inconsistent with the ∧ CDM model at 1σ confidence level （CL）, seem to support an evolutionary dark energy.Combining the current six BAO data and the reconstructed Hubble parameter from the original SNe la data, we obtain a tight constraint on the present matter density parameterΩm0in model-independent manner, find different data combinations give consistent results.