Gravitational lensing has long been used to measure or constrain cosmology models. Although the lensing effect of gravitational waves has not been observed by LIGO/Virgo, it is expected that there can be a few to a few hundred lensed events to be detected by the future Japanese space-borne interferometers DECIGO and B-DECIGO, if they are running for 4 years. Given the predicted lensed gravitational wave events, one can estimate the constraints on the cosmological parameters via the lensing statistics and the time delay methods. With the lensing statistics method, the knowledge of the lens redshifts, even with the moderate uncertainties, will set the tight bound on the energy density parameter ΩM for matter, that is, 0.288 ≲ ΩM ≲ 0.314 at best. The constraint on the Hubble constant H0 can be determined using the time delay method. It is found out that at 5σ, |δH0|/H0 ranges from $3{{\ \rm per\ cent}}$ to $11{{\ \rm per\ cent}}$ for DECIGO, and B-DECIGO will give less constrained results, $8{{\ \rm per\ cent}}\ \mathrm{ to}\ 15{{\ \rm per\ cent}}$. In this work, the uncertainties on the luminosity distance and the time delay distance are set to be $10{{\ \rm per\ cent}}$ and $20{{\ \rm per\ cent}}$, respectively. The improvement on measuring these distances will tighten the bounds.

中文翻译：

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使用 DECIGO 和 B-DECIGO 源从强透镜效应中约束宇宙学参数

引力透镜长期以来一直用于测量或约束宇宙学模型。虽然 LIGO/Virgo 没有观测到引力波的透镜效应，但预计未来日本的星载干涉仪 DECIGO 和 B-DECIGO 可以探测到几到几百个透镜事件，如果它们运行了4年。给定预测的透镜引力波事件，可以通过透镜统计和时间延迟方法估计对宇宙学参数的约束。使用透镜统计方法，即使具有中等不确定性，透镜红移的知识也会对物质的能量密度参数 ΩM 设置严格的界限，即最多为 0.288 ≲ ΩM ≲ 0.314。哈勃常数 H0 的约束可以使用时延法确定。发现在 5σ 处，|δH0|/H0 对于 DECIGO 的范围从 $3{{\ \rm per\ cent}}$ 到 $11{{\ \rm per\ cent}}$，而 B-DECIGO 将给出更少约束结果，$8{{\ \rm per\ cent}}\ \mathrm{ to}\ 15{{\ \rm per\ cent}}$。在这项工作中，光度距离和时延距离的不确定性分别设置为$10{{\ \rm per\ cent}}$和$20{{\ \rm per\ cent}}$。测量这些距离的改进将收紧界限。