Directly comparing the 6 expansion rate measured by type Ia supernovae data and the lower bound on the expansion rate set by the strong energy conditions or the null hypothesis that there never exists cosmic acceleration, we see $3\sigma$ direct evidence of cosmic acceleration and the $Rh=ct$ model is strongly excluded by the type Ia supernovae data. We also use Gaussian process method to reconstruct the expansion rate and the deceleration parameter from the 31 cosmic chronometers data and the 6 data points on the expansion rate measured from type Ia supernoave data, the direct evidence of cosmic acceleration is more than $3\sigma$ and we find that the transition redshift $z_t=0.60_{-0.12}^{+0.21}$ at which the expansion of the Universe underwent the transition from acceleration to deceleration. The Hubble constant inferred from the cosmic chronometers data with the Gaussian process method is $H_0=67.46\pm4.75$ Km/s/Mpc. To understand the properties of cosmic acceleration and dark energy, we fit two different two-parameter models to the observational data, and we find that the constraints on the model parameters from either the full distance modulus data by the Pantheon compilation or the compressed expansion rate data are very similar, and the derived Hubble constants are consistent with the Planck 2018 result. Our results confirm that the 6 compressed expansion rate data can replace the full 1048 distance modulus data from the Pantheon compilation. We derive the transition redshift $z_t=0.61_{-0.16}^{+0.24}$ by fitting a simple $q(z)$ model to the combination of cosmic chronometers data and the Pantheon compilation, the result is consistent with that obtained from the reconstruction with Gaussian process. Abridged.

中文翻译：

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宇宙加速和观测限制的证据

直接比较 Ia 型超新星数据测得的 6 膨胀率与强能量条件或宇宙加速不存在的原假设设定的膨胀率下界，我们看到了宇宙加速的 $3\sigma$ 直接证据和$Rh=ct$ 模型被 Ia 型超新星数据强烈排除。我们还使用高斯过程方法从31个宇宙天文台数据和Ia型超新星数据测量的膨胀率上的6个数据点重建膨胀率和减速参数，宇宙加速的直接证据超过$3\sigma$我们发现过渡红移 $z_t=0.60_{-0.12}^{+0.21}$ 在这个过渡中，宇宙的膨胀经历了从加速到减速的过渡。用高斯过程方法从宇宙天文钟数据推断出的哈勃常数为$H_0=67.46\pm4.75$Km/s/Mpc。为了理解宇宙加速度和暗能量的特性，我们将两个不同的双参数模型拟合到观测数据中，我们发现来自 Pantheon 编译的全距离模数数据或压缩膨胀率对模型参数的约束数据非常相似，导出的哈勃常数与普朗克 2018 年的结果一致。我们的结果证实，6 个压缩膨胀率数据可以替换来自 Pantheon 编译的完整 1048 个距离模数数据。我们通过将简单的 $q(z)$ 模型拟合到宇宙天文台数据和万神殿汇编的组合中，推导出红移过渡 $z_t=0.61_{-0.16}^{+0.24}$，结果与用高斯过程重建得到的结果一致。简略。