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

Abstract

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) [Formula: see text] from strong gravitational lensing (SGL) and the ratio of luminosity distance (LD) [Formula: see text] 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 [Formula: see text] and [Formula: see text] 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 [Formula: see text] 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.