We study the implications of the Planck temperature power spectrum at low multipoles, $\ell<1000$, and SPTPol data. We show that this combination predicts consistent lensing-induced smoothing of acoustic peaks within $\Lambda$CDM cosmology and yields the robust predictions of the cosmological parameters. Combining only the Planck large-scale temperature data and the SPTPol polarization and lensing measurements within $\Lambda$CDM model we found substantially lower values of linear matter density perturbation $\sigma_8$ which bring the late-time parameter $S_8=\sigma_8\sqrt{\Omega_m/0.3}=0.763\pm0.022$ into accordance with galaxy clustering and weak lensing measurements. It also raises up the Hubble constant $H_0=69.68\pm1.00{\rm \,\,km\,s^{-1}Mpc^{-1}}$ that reduces the Hubble tension to the $2.5\sigma$ level. We examine the residual tension in the Early Dark Energy (EDE) model which produces the brief energy injection prior to recombination. We implement both the background and perturbation evolutions of the scalar field which potential scales as $V(\phi)\propto \phi^{2n}$. Including cosmic shear measurements (KiDS, VIKING-450, DES) and local distance-ladder data (SH0ES) to the combined fit we found that EDE completely alleviates the Hubble tension while not degradating the fit to large-scale structure data. The EDE scenario significantly improves the goodness-of-fit by $2.9\sigma$ in comparison with the concordance $\Lambda$CDM model. The account for the intermediate-redshift data (the supernova dataset and baryon acoustic oscillation data) fits perfectly to our parameter predictions and indicates the preference of EDE over $\Lambda$CDM at $3\sigma$.

中文翻译：

---

普朗克和 SPTPol 数据的组合分析有利于早期的暗能量模型

我们研究了低多极点、$\ell<1000$ 和 SPTPol 数据下普朗克温度功率谱的含义。我们表明，这种组合预测了 $\Lambda$CDM 宇宙学中声波峰的一致透镜诱导平滑，并产生了对宇宙学参数的稳健预测。仅结合 $\Lambda$CDM 模型中的普朗克大尺度温度数据和 SPTPol 偏振和透镜测量，我们发现线性物质密度扰动 $\sigma_8$ 的值显着降低，这带来了后期参数 $S_8=\sigma_8\ sqrt{\Omega_m/0.3}=0.763\pm0.022$ 符合星系团聚和弱透镜测量。它还提高了哈勃常数 $H_0=69.68\pm1.00{\rm \,\,km\,s^{-1}Mpc^{-1}}$ 将哈勃张力降低到 $2.5\sigma$等级。我们检查了早期暗能量 (EDE) 模型中的残余张力，该模型在复合之前产生了短暂的能量注入。我们实现了标量场的背景和扰动演化，其潜在尺度为 $V(\phi)\propto \phi^{2n}$。包括宇宙剪切测量（KiDS、VIKING-450、DES）和局部距离阶梯数据（SH0ES）到组合拟合中，我们发现 EDE 完全减轻了哈勃张力，同时不会降低对大规模结构数据的拟合。与一致性 $\Lambda$CDM 模型相比，EDE 场景显着提高了 $2.9\sigma$ 的拟合优度。中间红移数据（超新星数据集和重子声学振荡数据）的说明完全符合我们的参数预测，并表明 EDE 在 $3\sigma$ 上优于 $\Lambda$CDM。