Lensing amplitude anomaly and varying electron mass alleviate the Hubble and $S_8$ tensions
Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台暗物质与空间天文重点实验室）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）
Yi-Ying Wang, Lei Lei, Shao-Peng Tang, Yi-Zhong Fan
备注：
28 pages, 7 figures, 6 tables. Added Planck PR4 likelihoods. Accepted for publication in JCAP
宇宙学测量揭示了标准ΛCDM模型内的矛盾，特别是哈勃常数和S8参数的不一致。一种涉及时间变化电子质量的修改再结合场景已被提出作为解决哈勃矛盾而不加剧S8矛盾的可行方案。最近的观测还揭示了其他可能偏离ΛCDM框架的现象，如非平坦的空间曲率和异常的CMB引力透镜幅度。在本研究中，我们探讨是否引入电子质量变化me，允许非零空间曲率ΩK，以及自由的引力透镜幅度Alens可以解决这些持续的矛盾。使用普朗克公共发布（PR）3和ACT功率谱，普朗克PR4和ACT引力透镜地图，以及DESI DR2的BAO测量，我们得到H0=69.61±0.60 km s⁻¹ Mpc⁻¹和S8=0.808±0.012，其中Δme/me=0.0109±0.0068和Alens=1.030±0.039，均超过ΛCDM预期。我们发现没有空间曲率偏离平坦的迹象，即使包括宇宙 chronometers和Ia型超新星样本。然而，当采用最新的普朗克功率谱似然性，NPIPE和HiLLiPoP，我们得到较低的电子质量，其中Δme/me=-0.0063±0.0095和-0.0095±0.0078，只缓解S8矛盾。引力透镜幅度仍然异常高，其中Alens=1.053±0.042和1.075±0.044。我们的结果指向一种有希望的宇宙学模型方向，以解决上述矛盾，尽管需要更精确的数据来澄清上述修改。
英文摘要：
Cosmological measurements have revealed tensions within the standard $Λ$CDM model, notably discrepancies in the Hubble constant and $S_8$ parameter. A modified recombination scenario involving a time-varying electron mass has been proposed as a feasible solution to the Hubble tension without exacerbating the $S_8$ tension. Recent observations have further revealed other potential deviations from the $Λ$CDM framework, such as non-flat spatial curvature and an anomalous CMB lensing amplitude. In this study, we explore whether introducing a variation in the electron mass $m_e$, allowing non-zero spatial curvature $Ω_K$, and a free lensing amplitude $A_{\rm lens}$ can resolve these persistent tensions. Using the Planck Public Release (PR) 3 and ACT power spectra, Planck PR4 and ACT lensing maps, together with BAO measurements from DESI DR2, we obtain $H_0 = 69.61^{+0.60}_{-0.55} \rm \, km \, s^{-1} \, Mpc^{-1}$ and $S_8= 0.808\pm0.012$, with $Δm_e / m_e = 0.0109^{+0.0068}_{-0.0066}$ and $A_{\rm lens} = 1.030^{+0.039}_{-0.037}$, both exceeding the $Λ$CDM expectations. We find no indication of spatial curvature deviating from flatness, even when including the Cosmic Chronometers and SNe Ia samples. However, when adopting the latest Planck power spectra likelihoods, NPIPE and HiLLiPoP, we obtain lower electron masses with $Δm_e / m_e = -0.0063^{+0.0095}_{-0.0099}$ and $-0.0095^{+0.0078}_{-0.0079}$, relieving the $S_8$ tension only. The lensing amplitude remains anomalously high, with $A_{\rm lens} = 1.053^{+0.042}_{-0.040}$ and $1.075^{+0.044}_{-0.043}$. Our results point to a promising direction for cosmological models to reconcile the aforementioned discrepancies, although more precise data from future experiments will be necessary to clarify the aforementioned modifications.
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Facultad de Ingeniería y Arquitectura, Universidad Central de Chile（智利中央大学工程与建筑学院）；Instituto de Astronomía, Observatorio Astronómico Nacional, Universidad Nacional Autónoma de México（墨西哥国立自治大学国家天文台天体物理研究所）
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