标题： 尺度不变真空范式：主要成果与最新进展 显示英文标题

标题： The Scale Invariant Vacuum Paradigm: main results and current progress

摘要： 我们总结了尺度不变真空（SIV）范式的主要结果，该范式与Weyl可积几何相关。在简要回顾数学框架之后，我们将重点介绍SIV中与膨胀相关的[9]、密度涨落增长[8]以及SIV在星系尺度不变动力学、MOND、暗物质和矮椭球星系中的应用[7]的主要结果。还讨论了弱场SIV结果与重新参数化范式中非适当时间参数化之间的联系[14]。 显示英文摘要

摘要： We present a summary of the main results within the Scale Invariant Vacuum (SIV) paradigm as related to the Weyl Integrable Geometry. After a brief review of the mathematical framework, we will highlight the main results related to inflation within the SIV [9], the growth of the density fluctuations [8], and the application of the SIV to scale-invariant dynamics of Galaxies, MOND, Dark Matter, and the Dwarf Spheroidals [7]. The connection of the weak-field SIV results to the un-proper time parametrization within the re-parametrization paradigm is also discussed [14].