Testing the Distance-Duality Relation from Strong Gravitational Lensing, Type Ia Supernovae and Gamma-Ray Bursts Data up to redshift $z\sim 3.6$

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) $D=D_{\mathrm{A}}^{\mathrm{sl}}/D_{\mathrm{A}}^{\mathrm{s}}$ from strong gravitational lensing (SGL) and the ratio of luminosity distance (LD) $D^{\ast }=D_{\mathrm{L}}^{\mathrm{l}}/D_{\mathrm{L}}^{\mathrm{s}}$ 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 $z_{\mathrm{s}}$ and $z_{\mathrm{l}}$ 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 $1\sigma$ 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.

18pages and 5figures

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