On Planck-Scale Remnants of Bouncing Cosmology Big Bang: Quantum Mechanics of Gravitational Super-Atoms and their Macro-Cosmological Implications

We formalize the quantum-mechanical spectrum, stability criteria, and macro-cosmological evolution of sub-Planckian super-atoms formed by stable fermionic remnants of extreme quantum black holes (EQBH) capturing supersymmetric partners. We analyze two distinct classes of primordial remnants: 1) Charged ionic super-atoms governed by a localized scalar selectron shell,2) Genuinely neutral super-atoms stabilized by a saturated cloud of Grand Unified Theory (GUT) scale scalar sneutrinos. Utilizing the Klein-Gordon-Fock and Gross-Pitaevskii formalisms in a curved Schwarzschild background, we derive the exact mass-energy profiles and physical dimensions for both structures. We demonstrate that while the ionic sector is strictly limited to single-charge states via an internal Coulomb blockade, the bosonic sneutrino shell experiences saturation at a finite Kaup-Ruffini-Bonazzola mass limit (M_max ≈ 0.29 g), preventing unphysical gravitational collapse. On macroscopic scales, the spatial volume averaging of the uncompensated U(1)_EM fields of the ionic sector generates a parameter-free dark energy alternative (with an equation of state parameter w → −1). Furthermore, we evaluate the cosmological signatures of these relics: the asynchronous nature of quantum transitions yields a wide-bandwidth low-frequency stochastic gravitational wave background centered at ν_0 ≈ 310.3 Hz. Finally, we formulate concrete terrestrial and planetary detection strategies, establishing that while the sharp gravitational tracks of naked cores can be resolved via cryogenic acoustic gradiometry, the macroscopically heavy neutral states offer a novel, alternative top-down paradigm for the nucleation core of atmospheric plasmoids, potentially contributing a quantum-gravitational channel to the multi-causal phenomenon of ball lightnings.