[论文解读] Canonical Hubble-Tension-Resolving Early Dark Energy Cosmologies are Inconsistent with the Lyman-$α$ Forest

Samuel Goldstein, J. Colin Hill+2 more|arXiv (Cornell University)|Mar 1, 2023

Cosmology and Gravitation Theories被引用 4

一句话总结

该论文表明，为解决哈勃张力而提出的规范早期暗能量（EDE）模型与莱曼-α森林数据不一致。利用SDSS eBOSS和X-Shooter/MIKE的莱曼-α森林通量功率谱测量，发现EDE模型需要比莱曼-α数据所偏好更高的标量谱指数 $n_s$，导致 $H_0 = 67.9^{+0.4}_{-0.4}$ km/s/Mpc（68%置信水平），与SH0ES测量结果存在超过4σ的张力。

ABSTRACT

Current cosmological data exhibit discordance between indirect and some direct inferences of the present-day expansion rate, $H_0$. Early dark energy (EDE), which briefly increases the cosmic expansion rate prior to recombination, is a leading scenario for resolving this "Hubble tension" while preserving a good fit to cosmic microwave background (CMB) data. However, this comes at the cost of changes in parameters that affect structure formation in the late-time universe, including the spectral index of scalar perturbations, $n_s$. Here, we present the first constraints on axion-like EDE using data from the Lyman-$α$ forest, i.e., absorption lines imprinted in background quasar spectra by neutral hydrogen gas along the line of sight. We consider two independent measurements of the one-dimensional Ly$α$ forest flux power spectrum, from the Sloan Digital Sky Survey (SDSS eBOSS) and from the MIKE/HIRES and X-Shooter spectrographs. We combine these with a baseline dataset comprised of Planck CMB data and baryon acoustic oscillation (BAO) measurements. Combining the eBOSS Ly$α$ data with the CMB and BAO dataset reduces the 95% confidence level (CL) upper bound on the maximum fractional contribution of EDE to the cosmic energy budget, $f_{ m EDE}$, from 0.07 to 0.03 and constrains $H_0=67.9_{-0.4}^{+0.4}$ km/s/Mpc (68% CL), with maximum a posteriori value $H_0=67.9$ km/s/Mpc. Similar results are obtained for the MIKE/HIRES and X-Shooter Ly$α$ data. Our Ly$α$-based EDE constraints yield $H_0$ values that are in $>4σ$ tension with the SH0ES distance-ladder measurement and are driven by the preference of the Ly$α$ forest data for $n_s$ values lower than those required by EDE cosmologies that fit Planck CMB data. Taken at face value, the Ly$α$ forest severely constrains canonical EDE models that could resolve the Hubble tension.

研究动机与目标

• 测试规范早期暗能量（EDE）模型是否与莱曼-α森林数据一致，这些模型通过在再组合之前提升膨胀速率来解决哈勃张力。
• 利用高精度的莱曼-α森林通量功率谱测量，约束EDE的最大能量贡献分数 $f_{\text{EDE}}$。
• 评估莱曼-α数据对较低 $n_s$ 值的偏好是否与EDE模型为拟合普朗克CMB数据所需更高 $n_s$ 值产生冲突。
• 在莱曼-α数据背景下，评估EDE所偏好 $H_0$ 值与SH0ES直接测量结果之间的张力。

提出的方法

• 使用 $n=3$ 的轴子样势能函数，以 $f_{\text{EDE}}$、$z_c$ 和 $\theta_i$ 参数化EDE模型，利用 CLASS_EDE 代码计算背景和线性扰动演化。
• 采用基于线性功率谱幅度 $\Delta_L^2$ 和斜率 $n_L$ 的压缩似然函数，其参考点为 $k_p = 0.009$ s/km 和 $z_p = 3$，并对天体物理不确定性进行边际化。
• 将eBOSS和X-Shooter/MIKE的莱曼-α数据与普朗克2018年CMB数据（TTTEEE，lowl+lowE，弱引力透镜）以及BOSS、SDSS MGS和6dFGS的BAO测量结果相结合。
• 使用马尔可夫链蒙特卡洛方法进行贝叶斯参数推断，以获得 $f_{\text{EDE}}$、$H_0$、$n_s$ 及其他宇宙学参数的后验约束。
• 通过后验比较和统计度量（特别是 $n_s$ 和 $H_0$ 的差异）量化数据集之间的张力。

Figure 1: Comparison of the best-fit linear matter power spectrum at $z_{p}=3$ from the EDE (grey) and $\Lambda$ CDM (orange) fits to the baseline CMB + BAO dataset with the best-fit $\Lambda$ CDM cosmologies for the eBOSS (blue) [ 30 ] and XQ-100 (red) Ly $\alpha$ forest datasets. Shaded bands indi

实验结果

研究问题

• RQ1 规范EDE模型能否在解决哈勃张力的同时与莱曼-α森林数据一致？
• RQ2 在宇宙学分析中纳入莱曼-α森林数据后，$f_{\text{EDE}}$ 的上限是多少？
• RQ3 莱曼-α森林数据是否偏好一个与EDE模型为拟合CMB数据所需更高 $n_s$ 值相冲突的标量谱指数 $n_s$？
• RQ4 纳入莱曼-α数据后，$H_0$ 的推断值及其与SH0ES测量结果的张力如何变化？

主要发现

• eBOSS莱曼-α森林数据的引入将 $f_{\text{EDE}}$ 的95%置信水平上限从0.07降低至0.03。
• 边际化的 $H_0$ 约束为 $67.9^{+0.4}_{-0.4}$ km/s/Mpc（68%置信水平），后验最大值为67.9 km/s/Mpc。
• 使用MIKE/HIRES和X-Shooter莱曼-α数据也得到相同约束，证实了在独立数据集上的稳健性。
• 莱曼-α数据偏好较低的 $n_s$，而EDE模型为拟合普朗克CMB数据所需更高的 $n_s$，造成根本性张力。
• 由此得到的 $H_0$ 值与SH0ES直接测量值 $73.04 \pm 1.04$ km/s/Mpc存在 >4σ 张力。
• eBOSS分析中 $\log_{10}(z_c)$ 的后验分布呈现双峰，源于 $n_s$ 与 $f_{\text{EDE}}$ 之间的权衡，低 $z_c$ 值更有利于低 $n_s$。

Figure 2: Marginalized posteriors for a subset of EDE and $\Lambda$ CDM parameters with and without Ly $\alpha$ data. The baseline dataset (grey) consists of Planck 2018 high- $\ell$ (TT+TE+EE) and low- $\ell$ (TT+EE) measurements, as well as BOSS DR12, SDSS MGS, and 6dFGS BAO data. Including eBOSS