In order to estimate cosmic curvature from cosmological probes like standard candles, one has to measure the luminosity distance \(D_L(z)\), its derivative with respect to redshift \(D'_L(z)\) and the expansion rate H(z) at the same redshift. In this paper, we study how such idea could be implemented with future generation of space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), in combination with cosmic chronometers providing cosmology-independent H(z) data. Our results show that for the Hubble diagram of simulated DECIGO data acting as a new type of standard siren, it would be able to constrain cosmic curvature with the precision of \(\varDelta \varOmega _k= 0.09\) with the currently available sample of 31 measurements of Hubble parameters. In the framework of the third generation ground-based gravitational wave detectors, the spatial curvature is constrained to be \(\varDelta \varOmega _k= 0.13\) for Einstein Telescope (ET). More interestingly, compared to other approaches aiming for model-independent estimations of spatial curvature, our analysis also achieve the reconstruction of the evolution of \(\varOmega _k(z)\), in the framework of a model-independent method of Gaussian processes (GP) without assuming a specific form. Therefore, one can expect that the newly emerged gravitational wave astronomy can become useful in local measurements of cosmic curvature using distant sources.

为了从像标准蜡烛这样的宇宙探测器中估计宇宙曲率，必须测量光度距离\（D_L（z）\），其相对于红移\（D'_L（z）\）和膨胀率H的导数（z）处于相同的红移。在本文中，我们研究了如何与下一代天基DECi-hertz干涉仪引力波天文台（DECIGO）结合提供与宇宙学无关的H（z）数据的宇宙天文钟一起实现这种想法。我们的结果表明，对于模拟的DECIGO数据的哈勃图作为一种新型的标准警笛，它将能够以以下精度限制宇宙曲率：\（\ varDelta \ varOmega _k = 0.09 \），带有当前可用的31个哈勃参数测量值样本。在第三代地基重力波探测器的框架中，对于爱因斯坦望远镜（ET），空间曲率被限制为\（\ varDelta \ varOmega _k = 0.13 \）。更有趣的是，与其他旨在模型无关的空间曲率估计的方法相比，我们的分析还在高斯过程的模型无关方法的框架内实现了\（\ varOmega _k（z）\）的演化的重建。（GP），但不采用特定形式。因此，可以预期的是，新出现的引力波天文学在使用遥远源对宇宙曲率进行局部测量中将变得有用。