Inflationary Dynamics and the Emergence of a Stable Resonance Ratio

This work develops a minimal two‑mode Hamiltonian model for the first nontrivial oscillation of a quasi–de Sitter background and shows that its internal frequency ratio becomes a quantum‑selected parameter during inflation. A localized feature in the inflaton potential generates a narrow environmental resonance at frequency \ (\*\), producing Hamiltonian‑sector decoherence that suppresses superpositions of different ratios. The resulting stability functional \ (S (r) \) has a unique maximum at the fixed point of the recurrence relation \ (r = 1 + 1/r\), yielding the preferred value \ (r\). This ratio becomes imprinted on the classical Hamiltonian and produces observable signatures, including an oscillatory bispectrum with characteristic scale \ (k = a endH/r_\) and amplitude \ (10^-2\). The mechanism provides a concrete, falsifiable link between early‑universe dynamics, environmental resonance, and late‑time cosmological observables.