The 2.07 Billion kg Quantum Gravitational Mass and Its Applications in Astrophysics and Cosmic Evolution

This paper introduces a quantum gravitational reference mass unit, \( M_{QG}\cong 2.07 \times 10^9 \) kg, derived from the proton’s electromagnetic-to-gravitational force ratio. Most interesting point is that, squared ratio of TOV mass limit and \( M_{QG} \)is equal to the electron’s electromagnetic-to-gravitational force ratio. Positioned between particle and astrophysical scales, it bridges quantum mechanics and gravity. Its Schwarzschild radius is \( 3.07 \times 10^{-18} \) m and is matching with the weak interaction range. It can be considered as a primordial galactic or stellar seed of size m having Hubble-Hawking temperature of \( 1.82 \times 10^{22} \) K. If ‘QG dot’ is assumed to be a stable seed, one can expect miracles in stellar evolution. Thus, with reference to ‘quantum dot’, it can be called as “Quantum-Gravitational (QG) dot”. We further propose a quantized stellar mass spectrum , analogous to quantum angular momentum eigenvalues. This parameter-free relation predicts key astrophysical bounds: hydrogen-burning threshold (n=1 ), Chandrasekhar limit (n=4 ), and Tolman-Oppenheimer-Volkoff limit (n=5 ). Notably, \( \frac{hbar c}{G M_{QG}} \)aligns with the Higgs mass ( 128 GeV), unifying nuclear physics, astrophysics, and quantum gravity. Beyond standard unification, we identify a super gravitational phase transition at a galactic baryonic mass of \( 2 \times 10^8 M_{Sun} \) , derived from the fine-structure constant, strong coupling constant and\( M_{QG} \). This threshold explains flat rotation curves without dark matter, connecting Quantum Chromodynamics parameters to galactic dynamics. Active Galactic Nuclei (AGN) and powerful Radio Galaxies typically seem to host black holes exceeding this Super Gravity threshold. It can be observed via stronger accretion and relativistic jets.