Testing the distance-duality relation from strong gravitational lensing, type Ia supernovae and gamma-ray bursts data up to redshift z ∼ 3.6

In this paper, 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 = DAsl/D As from strong gravitational lensing (SGL) and the ratio of luminosity distance (LD) D∗ = D Ll/D Ls obtained from the joint of type Ia supernovae (SNIa) Union2.1 compilation and the latest Gamma-Ray Bursts (GRBs) data, where the superscripts s and l correspond to the redshifts zs and zl 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 redshifts 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.