Planck Meets Hubble within Cosmological Natural Units and Frequency-Dependent Yukawa Potentials Bridging Gravity, QCD, and Nuclear Scales
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2026
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| _version_ | 1866901347130933248 |
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| author | Papou, Aliaksei |
| author_facet | Papou, Aliaksei |
| contents | <p>We extend the classical $cG\hbar$ natural units by incorporating the present-day Hubble constant $H_0$, yielding Planck-Hubble (PH) units that connect quantum-gravitational and cosmological scales. These hybrid units exhibit a striking numerical alignment with quantum chromodynamics (QCD) characteristic values ($\sim$ fm lengths, $\sim$100--300 MeV energies). We derive explicit formulas for base and derived quantities and propose an empirical relation tying the gravitational constant $G$ to QCD mass scales modulated by cosmic expansion.</p> <p>Building on a related phenomenological framework \cite{papou2026b}, we discuss how frequency-dependent Yukawa potentials mediated by a scalar field may provide a dynamical mechanism for unifying long-range gravity with short-range residual nuclear interactions, potentially explaining the PH--QCD coincidence and offering insights into emergent gravity or scale-dependent couplings. Numerical comparisons use CODATA 2018 and Planck 2018 data, with implications for the Hubble tension explored.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18595031 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Planck Meets Hubble within Cosmological Natural Units and Frequency-Dependent Yukawa Potentials Bridging Gravity, QCD, and Nuclear Scales Papou, Aliaksei <p>We extend the classical $cG\hbar$ natural units by incorporating the present-day Hubble constant $H_0$, yielding Planck-Hubble (PH) units that connect quantum-gravitational and cosmological scales. These hybrid units exhibit a striking numerical alignment with quantum chromodynamics (QCD) characteristic values ($\sim$ fm lengths, $\sim$100--300 MeV energies). We derive explicit formulas for base and derived quantities and propose an empirical relation tying the gravitational constant $G$ to QCD mass scales modulated by cosmic expansion.</p> <p>Building on a related phenomenological framework \cite{papou2026b}, we discuss how frequency-dependent Yukawa potentials mediated by a scalar field may provide a dynamical mechanism for unifying long-range gravity with short-range residual nuclear interactions, potentially explaining the PH--QCD coincidence and offering insights into emergent gravity or scale-dependent couplings. Numerical comparisons use CODATA 2018 and Planck 2018 data, with implications for the Hubble tension explored.</p> |
| title | Planck Meets Hubble within Cosmological Natural Units and Frequency-Dependent Yukawa Potentials Bridging Gravity, QCD, and Nuclear Scales |
| url | https://doi.org/10.5281/zenodo.18595031 |