We investigate whether the $4.4\sigma$ tension on $H_0$ between SH$_{0}$ES 2019 and Planck 2018 can be alleviated by a variation of Newton's constant $G_N$ between the early and the late Universe. This changes the expansion rate before recombination, similarly to the addition of $\Delta N_{\rm eff}$ extra relativistic degrees of freedom . We implement a varying $G_N$ in a scalar-tensor theory of gravity, with a non-minimal coupling of the form $(M^2+\beta \phi^2)R$. If the scalar $\phi$ starts in the radiation era at an initial value $\phi_I \approx 0.3 \, M_{Pl}$ and with $\beta\approx-0.8$, a dynamical transition occurs naturally around the epoch of matter-radiation equality and the field evolves towards zero at late times. As a consequence the $H_0$ tension between SH$_{0}$ES (2019) and Planck 2018+BAO decreases, as in $\Delta N_{\rm eff}$ models. However, mostly due to late-time constraints from Post-Newtonian (PN) local gravity, the tension is reduced only to 3.5$\sigma$ level. When including also the SH$_{0}$ES data in the fit, the varying $G_N$ model has $H_0=69.2_{-0.75}^{+0.62}$ and an improvement of $\Delta\chi^2=-3.6$ compared to $\Lambda$CDM, at the cost of 2 extra parameters. This corresponds to a decrease of $7_{-6}^{+3}$ percent in the value of $G_N$ from the radiation era to the present time. For comparison, we update the fit of the $\Delta N_{\rm eff}$ model to the same dataset. We find that the $\Delta N_{\rm eff}$ model performs better than the simplest varying $G_N$ scenario, with $H_0=70_{-0.95}^{+0.93}$ and $\Delta\chi^2=-5.5$. The $\Lambda$CDM limit of the $\Delta N_{\rm eff}$ model is disfavored at slightly more than 2$\sigma$, since $\Delta N_{\rm eff}=0.316_{-0.15}^{+0.15}$.

中文翻译：

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H0 张力：Δ GN vs. Δ Neff

我们调查了 SH$_{0}ES 2019 和 Planck 2018 之间 $H_0$ 上 $4.4\sigma$ 的紧张局势是否可以通过牛顿早期和晚期宇宙之间的常数 $G_N$ 的变化来缓解。这改变了重组前的膨胀率，类似于增加了 $\Delta N_{\rm eff}$ 额外的相对论自由度。我们在引力的标量张量理论中实现了变化的 $G_N$，具有 $(M^2+\beta\phi^2)R$ 形式的非最小耦合。如果标量 $\phi$ 在辐射时代以初始值 $\phi_I \approx 0.3 \, M_{Pl}$ 和 $\beta\approx-0.8$ 开始，则在物质时代自然发生动态跃迁- 辐射平等，该场在后期趋向于零。因此，SH$_{0}$ES (2019) 和 Planck 2018+BAO 之间的 $H_0$ 张力减小，如在 $\Delta N_{\rm eff}$ 模型中。然而，主要是由于后牛顿 (PN) 局部重力的后期限制，张力仅降低到 3.5$\sigma$ 水平。当拟合中还包括 SH$_{0}$ES 数据时，变化的 $G_N$ 模型具有 $H_0=69.2_{-0.75}^{+0.62}$ 和 $\Delta\chi^2 的改进=-3.6$ 与 $\Lambda$CDM 相比，以 2 个额外参数为代价。这相当于从辐射时代到现在，$G_N$ 的价值减少了 $7_{-6}^{+3}$%。为了比较，我们将 $\Delta N_{\rm eff}$ 模型的拟合更新到相同的数据集。我们发现 $\Delta N_{\rm eff}$ 模型比最简单的变化 $G_N$ 场景表现更好，$H_0=70_{-0.95}^{+0.93}$ 和 $\Delta\chi^2= -5.5 美元。$\Delta N_{\rm eff}$ 模型的 $\Lambda$CDM 限制不受欢迎，略高于 2$\sigma$，