Local Dynamical Effects of Scale Invariance: the Lunar Recession

Abstract

Scale invariance is expected in empty Universe models, while the presence of matter tends to suppress it. As shown recently, scale invariance is certainly absent in cosmological models with densities equal to or above the critical value ρc = 3(H0)2/(8πG). For models with densities below ρc, the possibility of limited effects remains open. If present, scale invariance would be a global cosmological property. Some traces could be observable locally. For the Earth-Moon two-body system, the predicted additional lunar recession would be increased by 0.92 cm/yr, while the tidal interaction would also be slightly increased. The Earth-Moon distance is the most systematically measured distance in the Solar System, thanks to the Lunar Laser Ranging (LLR) experiment active since 1970. The observed lunar recession from LLR amounts to 3.83 (±0.009) cm/yr; implying a tidal change of the length-of-the-day (LOD) by 2.395 ms/cy. However, the observed change of the LOD since the Babylonian Antiquity is only 1.78 ms/cy, a result supported by paleontological data, and implying a lunar recession of 2.85 cm/yr. The significant difference of (3.83-2.85) cm/yr = 0.98 cm/yr, already pointed out by several authors over the last two decades, corresponds well to the predictions of the scale-invariant theory, which is also supported by several other astrophysical tests.

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

“…In the late time Universe the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals [5] where one can find MOND to be a peculiar case of the SIV theory [6]. 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 [7].…”

“…Here, we add a few new sections, one on the possible differentiators of SIV from ΛCDM based on our earlier paper [10], with a specific emphasis on the distance moduli as function of the redshift, along with three new topic sections related to the recent developments in the application of SIV paradigm since our previous summary paper in 2022 [8]. The sections are on MOND as a peculiar case of the SIV theory [5], local dynamical effects within SIV as pertained to the lunar recession [7], and our latest study of the Big-Bang Nucleosynthesis (BBNS) within the SIV Paradigm [3].…”

“…The usual timescale τ in years or seconds is τ 0 = 13.8 Gyr at present [29] and τ in = 0 at the Big-Bang. One can change from the SIV-time t to the usual time scale τ by using the relationship ansatz [7]:…”

“…The last factor could be recognized as κ 0 (τ 0 ). To see this one can utilize the equations ( 22) and ( 23) to switch from the SIV-time t to the conventional time τ scale [7] in order to obtain:…”

“…where i ∈ 1, 2, 3, while the potential Φ = G t M/r is scale invariant and G t is the Newton's constant of gravity in SIV t-time units system (t 0 = 1) . When written in the usual units with present time τ 0 , based on (27) the modified Newton's equation ( 29) is then [6,7]:…”