本文利用最新的宇宙学数据集，结合相同红移下的光度距离 DL 和角 直径距离 DA，对距离对偶关系（DDR）进行了检验。对于 DL，本文使用 第三代引力波探测器爱因斯坦望远镜（the Einstein Telescope, ET），考虑模 拟其观测的引力波数据作为标准汽笛得到光度距离；对于 DA，文章通过甚 长基线干涉测量（VLBI）得到的致密类星体样本作为一种新的宇宙学标准 尺，得到角直径距离。由于不受宇宙中尘埃的吸收和散射影响，这提供了 结合引力波（GW）信号和电磁波（EM）信号在更高精度下直接检验 DDR 的方法。文章结果表明，结合现有射电类星体的观测数据，距离对偶关系 在 10?2 精度下得到了验证。

In this paper we analyse the implications of the latest cosmological data sets to test the Etherington’s distance duality relation, which connects the luminosity distance DL and angular diameter distance DA at the same redshift. For DL we consider the simulated data of gravitational waves from the third­generation gravitational wave detector (the Einstein Telescope, ET), which can be considered as standard siren, while the angular diameter distances DA are derived from the newly­compiled sample of compact radio quasars observed by very­long­baseline interferometry, which represents a type of new cosmological standard ruler. Alleviating the absorbtion and scattering effects of dust in the Universe, this will create a valuable opportunity to directly test DDR at much higher precision with the combination of gravitational wave and electromagnetic signals. Our results show that, with the combination of the current radio quasar observations, the duality­distance relation can be verified at the precision of 10−2 .