Title: Early dark energy, the Hubble-parameter tension, and the string axiverse Show Chinese title

Title: 早期暗能量，哈勃参数矛盾，以及弦论轴子多重宇宙

Abstract: Precise measurements of the cosmic microwave background (CMB) power spectrum are in excellent agreement with the predictions of the standard $\Lambda$CDM cosmological model. However, there is some tension between the value of the Hubble parameter $H_0$ inferred from the CMB and that inferred from observations of the Universe at lower redshifts, and the unusually small value of the dark-energy density is a puzzling ingredient of the model. In this paper, we explore a scenario with a new exotic energy density that behaves like a cosmological constant at early times and then decays quickly at some critical redshift $z_c$. An exotic energy density like this is motivated by some string-axiverse-inspired scenarios for dark energy. By increasing the expansion rate at early times, the very precisely determined angular scale of the sound horizon at decoupling can be preserved with a larger Hubble constant. We find, however, that the Planck temperature power spectrum tightly constrains the magnitude of the early dark-energy density and thus any shift in the Hubble constant obtained from the CMB. If the reionization optical depth is required to be smaller than the Planck 2016 $2\sigma$ upper bound $\tau\lesssim 0.0774$, then early dark energy allows a Hubble-parameter shift of at most 1.6 km~s$^{-1}$~Mpc$^{-1}$ (at $z_c\simeq 1585$), too small to fully alleviate the Hubble-parameter tension. Only if $\tau$ is increased by more than $5\sigma$ can the CMB Hubble parameter be brought into agreement with that from local measurements. In the process, we derive strong constraints to the contribution of early dark energy at the time of recombination---it can never exceed $\sim2\%$ of the radiation/matter density for $10 \lesssim z_c \lesssim 10^5$. Show Chinese abstract

Abstract: 精确测量宇宙微波背景（CMB）功率谱与标准 $\Lambda$冷暗物质宇宙学模型的预测高度一致。 然而，从CMB推导出的哈勃参数 $H_0$值与从低红移宇宙观测得到的值之间存在一些矛盾，而暗能量密度的异常小值是该模型中的一个令人困惑的成分。 在本文中，我们探讨了一种新的奇异能量密度情景，它在早期时间表现得像宇宙常数，并在某个临界红移 $z_c$处迅速衰减。 这种奇异的能量密度受到一些弦论-轴子多宇宙启发的暗能量情景的激励。 通过增加早期时间的膨胀率，可以在更大的哈勃常数下保留解耦时声学视差的精确确定的角度尺度。 然而，我们发现普朗克温度功率谱严格限制了早期暗能量密度的大小，因此也限制了从CMB获得的哈勃常数的任何变化。 如果再电离光学深度需要小于普朗克2016年$2\sigma$上限$\tau\lesssim 0.0774$，那么早期暗能量允许的哈勃参数偏移最多为1.6 km~s$^{-1}$~Mpc$^{-1}$（在$z_c\simeq 1585$时），小到无法完全缓解哈勃参数矛盾。只有当$\tau$增加超过$5\sigma$时，才能使CMB哈勃参数与本地测量结果一致。 在这一过程中，我们推导出对重组时期早期暗能量贡献的强约束——它在$10 \lesssim z_c \lesssim 10^5$时永远不能超过辐射/物质密度的$\sim2\%$。