Hubble-constant crisis

Cai Rong-Gen; Li Li; Wang Shao-Jiang

doi:10.7498/aps.72.20231270

Abstract

The Hubble constant quantitatively characterizes the expansion rate of the current Universe, and its precise measurement has become a crucial scientific problem. In recent years, there has been an increasingly serious discrepancy between the local direct measurements of the Hubble constant and the global fitting results, where the local direct measurements come from the local distance ladder measurements of the late universe, and the global fitting results come from fitting the standard model of cosmology to the microwave background radiation from the early universe. If this discrepancy is not caused by the observation error and systematic error of any of the observation methods, it probably means that there is a new physics beyond the existing standard model of cosmology. This article briefly reviews the Hubble constant problem from two aspects with observational and theoretical points of view, and finally provide a perspective view from both observational and theoretical aspects by combining the author’s research on this problem in recent years. The observational review includes cosmological observations from both early Universe (either depending or independent of the CMB measurements) and late Universe (either depending or independent of the distant-ladder measurements), and the theoretical review includes model buildings from modifying both early Universe (either recombination history or expansion history) and late Universe (either homogeneous modifications or inhomogeneous modifications). The final observational perspective includes both local and non-local cosmic variances with their Hubble residual correlated to the matter density contrasts of observer and sample, respectively, and the final theoretical perspective concludes the interacting dark energy model as the most promising candidate for both Hubble tension and S₈ tension, which can be specifically realized in a chameleon dark energy model, pointing to a scale-dependent effective cosmological constant.

Keywords:

Authors and contacts

1.
School of Physical Science and Technology, Ningbo University, Ningbo 315211, China
2.
Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
3.
School of Physical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing 100049, China
4.
Hangzhou Institute for Advanced Study (HIAS), University of Chinese Academy of Sciences (UCAS), Hangzhou 310024, China

Corresponding author: Wang Shao-Jiang, schwang@itp.ac.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFA0718304, 2021YFC2203004, 2020YFC2201502) and the National Natural Science Foundation of China (Grant Nos. 12105344, 12235019, 11821505, 11991052, 11947302, 12122513).

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Cited By

图 1 哈勃常数危机: 来自 CMB-Planck+$ \Lambda{\mathrm{CDM}} $的$ H_0 $限制(蓝色)与来自 SH0ES 合作组距离阶梯 SNe+Cepheid 的$ H_0 $测量(绿色)之间高达将近$ 5\sigma $的偏离. 图片来自文献[2]

Figure 1. The Hubble-constant tension: The nearly$ 5\sigma $discrepancy between the$ H_0 $constraint (blue) from CMB-Planck+$ \Lambda{\mathrm{CDM}}$ and the$ H_0 $measurement (green) from SH0ES group using the distance ladder SNe+Cepheid. The figure comes from Ref. [2].

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图 2 哈勃常数危机: 来自早期宇宙的间接拟合和晚期宇宙的直接测量. 图片来自文献[8]

Figure 2. The Hubble-constant tension: The indirect constraints from fitting the early Universe and direct measurements from the late Universe. The figure comes from Ref. [8].

DownLoad: Full-Size Img PowerPoint

图 3 把BBN与星系BAO(蓝色)和Lyman-$ \alpha $BAO(绿色)结合后给出的限制(红色)与Planck 2018 限制结果(紫色)和SH0ES组测量结果(橙色)的对比. 图片来自文献[18]

Figure 3. The comparison to the Planck 2018 constraint (purple) and the SH0ES measurement (orange) with respect to the joint constraint (red) from combing BBN with galaxy BAO (blue) and Lyman-$ \alpha $BAO (green). The figure comes from Ref. [18].

DownLoad: Full-Size Img PowerPoint

图 4 SH0ES 合作组采用的三级距离阶梯. 图片来自文献[2]

Figure 4. The three-rung distance ladder adopted by the SH0ES group. The figure comes from Ref. [2].

DownLoad: Full-Size Img PowerPoint

图 5 来自与距离阶梯无关的强引力透镜时间延迟对哈勃常数测量, 图片来自文献[18]

Figure 5. The Hubble-constant measurements from strong lensing time delay independent of distance ladders. The figure comes from Ref. [18].

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图 6 来自 LISA 和太极空间引力波探测器联网的对哈勃常数的暗汽笛限制. 图片来自文献[40]

Figure 6. The dark siren constraints on the Hubble constant from the LISA-Taiji network. The figure comes from Ref. [40]

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图 7 星系弱引力透镜观测(左上)、SH0ES组对$ H_0 $的测量(左中)以及重子声学振荡观测(左下)对早期宇宙模型(右)的限制. 图片来自文献[12]

Figure 7. The constraints (left) on the early-Universe models (right) from the galactic weak lensing observation (left top), the SH0ES measurement on$ H_0 $(left medium), and the BAO observation (left bottom). The figure comes from Ref. [12].

DownLoad: Full-Size Img PowerPoint

图 8 在$ \Lambda{\mathrm{CDM}} $ 模型及其PAge/MAPAge参数化模型以及按红移$ z $和$ y = 1 - a $的泰勒展开近似下的BAO特征尺度(红、蓝、绿)与BAO观测数据的对比. 图片来自文献[14]

Figure 8. The comparison of characteristic BAO length scales to the BAO data from the$ \Lambda {\mathrm{CDM}}$ model and its PAge/MAPAge parameterization models as well as its Taylor expansion models in redshift$ z $and$ y=1-a $. The figure comes from Ref. [14].

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图 9 变色龙暗能量机制示意图　(a) 变色龙暗能量有效势$ V_{\rm{eff}}(\varphi) = V(\varphi) + U(\varphi) $, 其中变色龙场势函数取 Peebles-Ratra 势函数$ V(\varphi) = \alpha\varLambda^4(\varLambda/\varphi)^n $, 变色龙耦合项取伸缩子耦合$ U(\varphi) = \exp(\varphi/\varLambda)\hat{\rho}_{\rm{m}} $. 易见当实线对应的物质密度$ \hat{\rho}_{\rm{m}} $大于虚线对应的物质密度时, 相应地实线在有效势的真空期望值处对应的势函数值(真空能)也大于虚线的情况. (b) 选取 Planck 2018 测量结果(红色)为背景宇宙学, 那么局域物质密度超出(纵轴)对应的局域哈勃常数(横轴)可以拟合 SH0ES 测量结果(蓝色). 图片来自文献[88]

Figure 9. The illustrative demonstration of the chameleon dark energy model. (a) The effective potential of chameleon dark energy is$ V_{\rm{eff}}(\varphi) = V(\varphi) + U(\varphi) $, where the chameleon potential is of Peebles-Ratra form$ V(\varphi) = \alpha\varLambda^4(\varLambda/\varphi)^n $, and the chameleon coupling is of dilaton form$ U(\varphi) = \exp(\varphi/\varLambda)\hat{\rho}_{\rm{m}} $. It is easy to see that when the solid curve corresponds to higher matter density$ \hat{\rho}_{\rm{m}} $than the dashed curve with lower one, then the potential energy (vacuum energy) at the vacuum expectation value of the effective potential is also higher than the dashed case. (b) Choosing the Planck 2018 result (red) as the background cosmology, then the corresponding local Hubble constant (horizontal axis) from given local matter density contrast (vertical axis) could fit the SH0ES result (blue). The figure comes from Ref. [88].

DownLoad: Full-Size Img PowerPoint

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