The Cosmic Distance Duality Relation with Strong Lensing and Gravitational Waves: An Opacity-free Test

The cosmic distance duality relation (CDDR) is a fundamental rule in cosmological studies. Given the redshift z, it relates luminosity distance D ^L with angular diameter distance D ^A through {(1+z)}²{D}^A/{D}^L\equiv 1. Many efforts have been made to test CDDR with various observational approaches. However, to the best of our knowledge, those methods are always affected by cosmic opacity, which could violate CDDR owing to the non-conservation of photon number. Such a mechanism is more related to astroparticle physics. In this work, in order to directly study the nature of spacetime, i.e., to disentangle it from astroparticle physics, we propose a new strategy to test CDDR, with strong lensing providing D ^A and gravitational waves (GWs) providing D ^L . It is known that the propagation of GWs is unaffected by cosmic opacity. We demonstrate that distances from observations of optical lensing are also opacity-free. These two kinds of distance measurements make it possible to test spacetime. Our results show that the constraints on the deviations of CDDR will be very competitive with current techniques.