Elucidating the Dark Energy and Dark Matter Phenomena Within the Scale-Invariant Vacuum (SIV) Paradigm

The enigmatic phenomenon of dark energy (DE) is the elusive entity driving the accelerated expansion of our Universe. A plausible candidate for DE is the non-zero Einstein Cosmological Constant ΛE manifested as a constant energy density of the vacuum, yet it seemingly defies gravitational effects. In this work, we interpret the non-zero ΛE through the lens of scale-invariant cosmology. We revisit the conformal scale factor λ and its defining equations within the Scale-Invariant Vacuum (SIV) paradigm. Furthermore, we address the profound problem of the missing mass across galactic and extragalactic scales by deriving an MOND-like relation, g∼a0gN, within the SIV context. Remarkably, the values obtained for ΛE and the MOND fundamental acceleration, a0, align with observed magnitudes, specifically, a0≈10−10ms−2 and ΛE≈1.8×10−52m−2. Moreover, we propose a novel early dark energy term, T˜μν∼κH, within the SIV paradigm, which holds potential relevance for addressing the Hubble tension.