The Scale-Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II) ^†

This is a summary of the main results within the Scale-Invariant Vacuum (SIV) paradigm based on Weyl integrable geometry. We also review the mathematical framework and utilize alternative derivations of the key equations based on the reparametrization invariance as well. The main results discussed are related to the early universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. Some of the key SIV results for the early universe are a natural exit from inflation within the SIV in a later time $t_{\mathrm{exit}}$ with value related to the parameters of the inflationary potential along with the possibility for the density fluctuations to grow sufficiently fast within the SIV without the need for dark matter to seed the growth of structure in the universe. In the late-time universe, the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and dwarf spheroidals, where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth–Moon system.