Thyra-Hopf Detuning Theory (THDT): A Geometric Framework for Gravity, Particle Physics, and Cosmology from a Vibrational Substrate on the Hopf Fibration

Abstract

Thyra-Hopf Detuning Theory (THDT) proposes that gravity, the Standard Model, dark matter, dark energy, and cosmology emerge from a single multicomponent real scalar field on a compact internal S³ equipped with the Hopf fibration. The sole free parameter is the Bower Constant ⟨δ⟩/ω̄ ≈ 0.015, adopted as a fixed empirical coupling parameter that is geometrically motivated by volume-averaged projections of the left-invariant Maurer–Cartan 1-forms. The theory recovers Newtonian gravity in the weak field, resolves black-hole singularities via vibrational diffusion, predicts a +1.5% shift in the dominant quasinormal damping time and a −1.5% shift in Hawking temperature, generates fermion mass hierarchies from mode-overlap integrals, produces dynamical dark energy of the form w(z) = −1 + 0.05z, and modifies the redshift–time relation, yielding a factor ≈2.3 more evolutionary time at z ≈ 14.44. All results are controlled by the single geometric parameter. The framework is confronted with DESI DR2 / DES Year 6, H0DN, JWST MoM-z14, LVK GW250114, ACT DR6, and Planck 2018 data.