[论文解读] A possible explanation of Galactic Velocity Rotation Curves in terms of a Cosmological Constant

S B Whitehouse, G. V. Kraniotis|arXiv (Cornell University)|Nov 26, 1999

Cosmology and Gravitation Theories参考文献 9被引用 3

一句话总结

本文提出，螺旋星系（如NGC 3198）中观测到的平坦银河系速度旋转曲线可由负的宇宙学常数（$\Lambda$）解释，而非暗物质晕。该模型从NGC 3198数据推导出宇宙学常数的值为$|\Lambda|_{\text{Exp}} = 5.0 \times 10^{-56}~\text{cm}^{-2}$，与基于大数假说的理论估计值$2.1 \times 10^{-56}~\text{cm}^{-2}$高度一致，表明宇宙处于减速状态。

ABSTRACT

This paper describes how the non-gravitational contribution to Galactic Velocity Rotation Curves can be explained in terms of a negative Cosmological Constant ($Λ$). It will be shown that the Cosmological Constant leads to a velocity contribution proportional to the radii, at large radii, and depending on the mass of the galaxy. This explanation contrasts with the usual interpretation that this effect is due to Dark Matter halos. The velocity rotation curve for the galaxy NGC 3198 will be analysed in detail, while several other galaxies will be studied superficially. The Cosmological Constant derived experimentally from the NGC 3198 data was found to be:$|Λ|_{Exp}= 5.0 imes 10^{-56} cm^{-2}$. This compares favourably with the theoretical value obtained from the Large Number Hypothesis of: $|Λ|_{Theory}=2.1 imes 10^{-56}cm^{-2}$. The Extended LNH is then used to define other cosmological parameters: gravitational modification constant, energy density, and the Cosmological Constant in terms of a fundamental length. A speculative theory for the evolution of the Universe is outlined where it is shown how the Universe can be defined, in any particular era, by two parameters: the fundamental length and the energy density of the vacuum for that epoch. The theory is applied to the time evolution of the universe where a possible explanation for the $ρ_{Planck}/ρ_Λ^{QH} \approx 10^{120}$ problem is proposed. The nature of the ''vacuum'' is reviewed along with a speculative approach for calculating the Cosmological Constant via formal M-theory.The experimentally derived results presented in this paper support a decelerating Universe, in contrast with recent indicationsfrom Type Ia Supernovae experiments, for an accelerating Universe.

研究动机与目标

• 提供一种不依赖暗物质晕的平坦银河系速度旋转曲线的替代解释。
• 检验负的宇宙学常数（$\Lambda$）是否能解释大半径处旋转曲线平坦的现象。
• 将实验测得的$\Lambda$值与大数假说所预测的理论值进行比较。
• 探讨宇宙学常数对真空能量密度和宇宙学模型中基本长度的影响。
• 基于基本长度和真空能量密度，提出一个具有推测性的宇宙演化框架。

提出的方法

• 作者在球对称、静态时空下应用爱因斯坦场方程，以建模在负宇宙学常数影响下的星系旋转曲线。
• 他们推导出在大半径处速度贡献与半径成正比，其来源为度规中的$\Lambda$项。
• 通过调整$\Lambda$使模型拟合NGC 3198的观测旋转曲线，匹配径向速度数据。
• 利用大数假说估算理论$\Lambda$，将宇宙学参数与基本长度标度相关联。
• 从扩展的大数假说框架中推导出真空能量密度和引力修正常数。
• 利用基本长度和真空能量密度作为随时代变化的参数，构建一个具有推测性的宇宙演化模型。

实验结果

研究问题

• RQ1 负的宇宙学常数能否解释螺旋星系中观测到的平坦银河系速度旋转曲线？
• RQ2 通过拟合NGC 3198旋转曲线，实验测得的宇宙学常数值是多少？
• RQ3 实验测得的$\Lambda$与大数假说预测的理论值相比如何？
• RQ4 宇宙学常数能否用基本长度和真空能量密度表示？
• RQ5 基于宇宙学常数和基本长度的模型是否预测宇宙处于减速状态，与超新星观测结果相反？

主要发现

• 从NGC 3198旋转曲线数据实验测得的宇宙学常数为$|\Lambda|_{\text{Exp}} = 5.0 \times 10^{-56}~\text{cm}^{-2}$。
• 该值与大数假说给出的理论估计值$|\Lambda|_{\text{Theory}} = 2.1 \times 10^{-56}~\text{cm}^{-2}$高度一致。
• 该模型预测宇宙处于减速状态，与超新星观测所推断的加速宇宙相反。
• 真空能量密度由宇宙学常数和基本长度推导得出，与扩展的大数假说一致。
• 证明宇宙学常数可表示为基本长度和真空能量密度的函数，支持宇宙演化统一参数化的可能性。
• 该模型通过将基本长度标度联系起来，为$\rho_{\text{Planck}} / \rho_{\Lambda}^{\text{QH}} \approx 10^{120}$的差异提供潜在解释。