[论文解读] Difficulties in reconciling non-negligible differences between the local and cosmological values of the gravitational coupling in extended Brans-Dicke theories

Adrià Gómez Valent, Prajwal Hassan Puttasiddappa|arXiv (Cornell University)|May 31, 2021

Cosmology and Gravitation Theories参考文献 66被引用 4

一句话总结

本文研究了具有屏蔽机制的扩展布兰斯-迪克理论是否能够调和宇宙学中观测到的4–9%更高的有效引力耦合与本地测量的牛顿常数值之间的矛盾。尽管探讨了各种屏蔽机制，研究发现它们仅能产生可忽略的偏差——不足以在不违反太阳系约束的前提下解释$H_0$和$\sigma_8$之间的张力。

ABSTRACT

Recent studies by Sola Peracaula, Gomez-Valent, de Cruz Perez and Moreno-Pulido (2019,2020) have pointed out the intriguing possibility that Brans-Dicke cosmology with constant vacuum energy density (BD-$\Lambda$CDM) may be able to alleviate the $H_0$ and $\sigma_8$ tensions that are found in the framework of the concordance cosmological model (GR-$\Lambda$CDM). The fitting analyses presented in these works indicate a preference for values of the effective gravitational coupling appearing in the Friedmann equation, $G$, about $4-9\%$ larger than Newton's constant (as measured on Earth), and mildy evolving with the expansion of the universe. The signal reaches the $\sim 3.5\sigma$ c.l. when the prior on $H_0$ from SH0ES and the angular diameter distances to strong gravitationally lensed quasars measured by H0LICOW are considered, and the $\sim 3\sigma$ c.l. when only the former is included. Thus, the improvement in the description of the cosmological datasets relies on the existence of a mechanism capable of screening the modified gravity effects at those scales where deviations from standard General Relativity (GR) are highly constrained, as in the Solar System. In this paper we explore several extensions of BD-$\Lambda$CDM that can leave the cosmological evolution basically unaltered at the background and linear perturbations level, while being able to screen the Brans-Dicke effects inside the regions of interest, leading to standard GR. We search for weak-field solutions around spherical static massive objects with no internal pressure and show that, unfortunately, these mechanisms can only explain very tiny departures of the effective cosmological gravitational coupling from the one measured locally. This might hinder the ability of BD-$\Lambda$CDM to alleviate the cosmological tensions.

研究动机与目标

• 评估扩展布兰斯-迪克理论是否能够解决$\Lambda$CDM模型中观测到的$H_0$和$\sigma_8$张力。
• 研究屏蔽机制能否在太阳系中抑制修正引力效应，同时在宇宙学背景下允许增强的引力耦合。
• 确定弱场解在静态、非压强物体周围是否能再现所需的宇宙学偏差，而不违反本地引力约束。
• 在现实的屏蔽情景下，评估BD-$\Lambda$CDM作为解决宇宙学张力的可行方案。

提出的方法

• 推导扩展布兰斯-迪克理论中球对称、静态、非压强大质量物体的弱场解。
• 应用在高密度环境（如太阳系）中抑制偏离广义相对论的屏蔽机制。
• 分析弱场极限下的有效引力耦合，以比较宇宙学值与本地测量值。
• 在场方程中使用无迹条件，以确保与BD-$\Lambda$CDM背景演化的自洽性。
• 将预测的引力势与太阳系实验的观测约束进行比较。
• 对弱场区域中与牛顿常数的偏差进行数值评估。

实验结果

研究问题

• RQ1 具有屏蔽机制的扩展布兰斯-迪克理论能否产生比牛顿常数大4–9%的宇宙学引力耦合？
• RQ2 屏蔽机制在多大程度上能抑制太阳系中偏离广义相对论的效应，同时保持宇宙学修正？
• RQ3 在弱场、静态、球对称解中，有效引力耦合与牛顿常数的最大可能偏差是多少？
• RQ4 本地引力实验的约束在多大程度上限制了BD-$\Lambda$CDM在解决宇宙学张力方面的可行性？
• RQ5 观测到的约3.5$\sigma$的增强$G$偏好是否能与本地测量结果相容？

主要发现

• 本文探讨的屏蔽机制仅能产生有效引力耦合与牛顿常数之间微不足道的偏差，不足以解释宇宙学数据中观测到的4–9%增强。
• 在静态、非压强物体周围的弱场解与标准引力的偏离可忽略不计，无法达到所需的宇宙学信号。
• 弱场区域允许的最大偏差不足以在不违反太阳系约束的前提下调和$H_0$和$\sigma_8$张力。
• 即使采用SH0ES和H0LICOW提供的有利先验，屏蔽机制仍无法在宇宙学尺度上产生所需$G$的增强。
• 结果表明，除非引入超出所考虑屏蔽机制的新物理，否则BD-$\Lambda$CDM可能无法作为解决宇宙学张力的可行方案。