We apply Gaussian processes (GP) in order to impose constraints on teleparallel gravity and its $f(T)$ extensions. We use available $H(z)$ observations from (i) cosmic chronometers data (CC); (ii) Supernova Type Ia (SN) data from the compressed Pantheon release together with the CANDELS and CLASH Multi-Cycle Treasury programs; and (iii) baryonic acoustic oscillation (BAO) datasets from the Sloan Digital Sky Survey. For the involved covariance functions, we consider four widely used choices, namely the square exponential, Cauchy, Matern and rational quadratic kernels, which are consistent with one another within 1$\sigma$ confidence levels. Specifically, we use the GP approach to reconstruct a model-independent determination of the Hubble constant $H_0$, for each of these kernels and dataset combinations. These analyses are complemented with three recently announced literature values of $H_0$, namely (i) Riess $H_0^{\rm R} = 74.22 \pm 1.82 \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$; (ii) H0LiCOW Collaboration $H_0^{\rm HW} = 73.3^{+1.7}_{-1.8} \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$; and (iii) Carnegie-Chicago Hubble Program $H_0^{\rm TRGB} = 69.8 \pm 1.9 \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$. Additionally, we investigate the transition redshift between the decelerating and accelerating cosmological phases through the GP reconstructed deceleration parameter. Furthermore, we reconstruct the model-independent evolution of the dark energy equation of state, and finally reconstruct the allowed $f(T)$ functions. As a result, the $\Lambda$CDM model lies inside the allowed region at 1$\sigma$ in all the examined kernels and datasets, however a negative slope for $f(T)$ versus $T$ is slightly favored.

中文翻译：

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通过高斯过程约束远平行引力

我们应用高斯过程 (GP) 来对遥平行引力及其 $f(T)$ 扩展施加约束。我们使用来自 (i) 宇宙天文台数据 (CC) 的可用 $H(z)$ 观测值；(ii) 来自压缩万神殿发布的超新星 Ia 型 (SN) 数据以及 CANDELS 和 CLASH 多周期财政部计划；(iii) 来自斯隆数字巡天的重子声振荡 (BAO) 数据集。对于涉及的协方差函数，我们考虑了四种广泛使用的选择，即平方指数、Cauchy、Matern 和有理二次核，它们在 1$\sigma$ 置信水平内彼此一致。具体来说，我们使用 GP 方法为这些内核和数据集组合中的每一个重建哈勃常数 $H_0$ 的模型独立确定。这些分析补充了最近公布的 $H_0$ 的三个文献值，即 (i) Riess $H_0^{\rm R} = 74.22 \pm 1.82 \,{\rm km\, s}^{-1} {\ rm Mpc}^{-1}$; (ii) H0LiCOW 协作 $H_0^{\rm HW} = 73.3^{+1.7}_{-1.8} \,{\rm km\, s}^{-1} {\rm Mpc}^{-1} $; (iii) 卡内基-芝加哥哈勃计划 $H_0^{\rm TRGB} = 69.8 \pm 1.9 \,{\rm km\, s}^{-1} {\rm Mpc}^{-1}$。此外，我们通过 GP 重建的减速参数研究了减速和加速宇宙学阶段之间的过渡红移。此外，我们重建了暗能量状态方程的独立于模型的演化，最后重建了允许的 $f(T)$ 函数。因此，$\Lambda$CDM 模型位于所有检查的内核和数据集中 1$\sigma$ 的允许区域内，