Applying the distance sum rule in strong gravitational lensing (SGL) and type Ia supernova (SN Ia) observations, one can provide an interesting cosmological model-independent method to determine the cosmic curvature parameter $\Omega_k$. In this paper, with the newly compiled data sets including 161 galactic-scale SGL systems and 1048 SN Ia data, we place constraints on $\Omega_k$ within the framework of three types of lens models extensively used in SGL studies. Moreover, to investigate the effect of different mass lens samples on the results, we divide the SGL sample into three sub-samples based on the center velocity dispersion of intervening galaxies. In the singular isothermal sphere (SIS) and extended power-law lens models, a flat universe is supported with the uncertainty about 0.2, while a closed universe is preferred in the power-law lens model. We find that the choice of lens models and the classification of SGL data actually can influence the constraints on $\Omega_k$ significantly.

中文翻译：

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来自强引力透镜和 SN Ia 观测对空间曲率的宇宙学模型独立约束

在强引力透镜（SGL）和 Ia 型超新星（SN Ia）观测中应用距离和规则，可以提供一种有趣的独立于宇宙学模型的方法来确定宇宙曲率参数 $\Omega_k$。在本文中，新编译的数据集包括 161 个银河尺度 SGL 系统和 1048 个 SN Ia 数据，我们在 SGL 研究中广泛使用的三种透镜模型的框架内对 $\Omega_k$ 进行了限制。此外，为了研究不同质量透镜样本对结果的影响，我们根据介入星系的中心速度色散将 SGL 样本分为三个子样本。在奇异等温球 (SIS) 和扩展幂律透镜模型中，一个平坦的宇宙被支持，不确定性约为 0.2，而封闭的宇宙在幂律透镜模型中更受欢迎。我们发现镜头模型的选择和 SGL 数据的分类实际上可以显着影响 $\Omega_k$ 的约束。