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 \(ω\*\), 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 \(k = a{ end}H/r_\) and amplitude \(ε ~ 10⁻²\). The mechanism provides a concrete, falsifiable link between early‑universe dynamics, environmental resonance, and late‑time cosmological observables.