We investigate the relationship between the cosmic curvature and the model of dark energy (hereafter DE) with the recent Type Ia supernovae (hereafter SNe Ia) data, i.e., the Pantheon sample including 1048 SNe Ia with $0.01 < z < 2.3$. We obtain the measurements of the dimensionless spatial curvature density today, i.e., $\Omega_{k0} = -0.062^{+0.189}_{-0.169}, -0.004^{+0.228}_{-0.134}, 0.127^{+0.280}_{-0.276}$ and $0.422^{+0.213}_{-0.338}$ at 68\% confidence level (CL), respectively, in the scenarios of $\Lambda$CDM, $\phi$CDM (i.e., scalar field dark energy), $\omega$CDM and $\omega_0\omega_a$CDM models. In the scenario of $\Lambda$CDM model, a closed universe is preferred by the Pantheon sample, which is consistent with that from the Planck CMB spectra. However, the uncertainty of $\Omega_{k0}$ from the Pantheon SNe sample is about 8 times larger than that from the Planck data, so the former one supports a closed universe at a much lower CL than that from the latter one. An open unverse is supported by the Pantheon sample at $\sim$32\% and $\sim$78\% CLs, respectively, in the $\omega$CDM and $\omega_0\omega_a$CDM models. Among these models, the $\phi$CDM model is the one which supports the flat universe most strongly. It shows that $\Omega_{k0}$ is significantly dependent on the adopted model of dark energy, and there is a negative correlation between $\Omega_{k0}$ and the equation of state of DE.

中文翻译：

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用最新的超新星样本研究宇宙曲率和暗能量模型之间的关系

我们研究了宇宙曲率和暗能量模型（以下简称 DE）与最近的 Ia 型超新星（以下简称 SNe Ia）数据之间的关系，即万神殿样本包括 1048 个 SNe Ia，$0.01 < z < 2.3$。我们今天得到了无量纲空间曲率密度的测量值，即 $\Omega_{k0} = -0.062^{+0.189}_{-0.169}, -0.004^{+0.228}_{-0.134}, 0.127^{ +0.280}_{-0.276}$ 和 $0.422^{+0.213}_{-0.338}$ 分别在 68\% 置信水平 (CL) 下，在 $\Lambda$CDM、$\phi$CDM (即标量场暗能量）、$\omega$CDM 和 $\omega_0\omega_a$CDM 模型。在$\Lambda$CDM 模型的场景中，万神殿样本更喜欢封闭的宇宙，这与普朗克CMB 光谱一致。然而，Pantheon SNe样本的$\Omega_{k0}$的不确定性比普朗克数据的不确定性大8倍左右，因此前者支持封闭宇宙的CL比后者低得多。在 $\omega$CDM 和 $\omega_0\omega_a$CDM 模型中，Pantheon 样本分别在 $\sim$32\% 和 $\sim$78\% CLs 处支持开放宇宙。在这些模型中，$\phi$CDM 模型是最有力地支持平坦宇宙的模型。表明$\Omega_{k0}$显着依赖于所采用的暗能量模型，$\Omega_{k0}$与DE的状态方程呈负相关。在 $\omega$CDM 和 $\omega_0\omega_a$CDM 模型中，Pantheon 样本分别在 $\sim$32\% 和 $\sim$78\% CLs 处支持开放宇宙。在这些模型中，$\phi$CDM 模型是最有力地支持平坦宇宙的模型。表明$\Omega_{k0}$显着依赖于所采用的暗能量模型，$\Omega_{k0}$与DE的状态方程呈负相关。在 $\omega$CDM 和 $\omega_0\omega_a$CDM 模型中，Pantheon 样本分别在 $\sim$32\% 和 $\sim$78\% CLs 处支持开放宇宙。在这些模型中，$\phi$CDM 模型是最有力地支持平坦宇宙的模型。表明$\Omega_{k0}$显着依赖于所采用的暗能量模型，$\Omega_{k0}$与DE的状态方程呈负相关。