Vibrational Fragmentation Theory of the Gravitonium and Unified Origin of Λ and ULDM

We propose a speculative cosmological model based on a five-dimensional scalar field, termed the Gravitonio, whose quantized vibrational fragmentation generates a fractal multiverse of distinct realities, each defined by unique physical constants and laws. The vibrational modes follow a Fibonacci progression, with frequency ratios \omega_{n+1}/\omega_n \approx 1.618, reflecting intrinsic fractal autosimilarity and a fractal dimension D_f \approx 1.62 as confirmed by numerical simulations. This structure serves as a unifying principle, linking dark energy (\Lambda) and ultra-light dark matter (ULDM) to specific vibrational states of the Gravitonio, with ULDM masses estimated at \sim 10^{-22} \, \text{eV}, consistent with axion-like particle candidates. Quantum entanglement is modeled as a non-local interaction between fractal realities, mediated by coupling terms g_{ij} \sim 10^{-5} in the field’s action, while the observer’s role is hypothesized as stabilizing reality by collapsing wave functions onto specific modes. The model integrates Loop Quantum Gravity (LQG), where the entropy of black holes may correlate with the density of vibrational modes, and String Theory, with the extra dimension w interpreted as a compactified scale (\sim 10^{-10} \, \text{m}). Advanced numerical simulations on a 512^4 \times 128 grid, employing pseudo-spectral methods, validate the Fibonacci progression and predict fractal patterns in the cosmic microwave background (CMB) at multipole scales \ell \sim 200, 500, 800. These predictions are testable via targeted CMB analyses at \ell \sim 500 and large-scale structure (LSS) data, supported by comparisons with Planck 2018 and future Simons Observatory results. This framework invites further observational validation and theoretical refinement, positioning the Gravitonio as a candidate for unifying cosmological phenomena within a higher-dimensional context.