Quantum Parametric Cosmogenesis Theory

We derive the resonant non-Gaussianity generated by a discrete-scale-invariant (DSI) modulationduring single-field slow-roll inflation, focusing on the specific case where the log-frequency is fixedby the golden ratio ϕ = (1 + √5)/2. The DSI condition P (kϕ) = P (k) implies a log-periodicmodulation with angular frequency ω = 2π/ ln ϕ ≃ 13.05. Using the in-in formalism, we computethe leading cubic interaction induced by a small oscillatory modulation of the potential and derivethe resonant bispectrum template. We obtain the amplitude scaling f resNL ∼ ϵosc ω (up to slow-rollfactors), where ϵosc ≪ 1 controls the oscillation strength. We map the signal to CMB multipolesand provide order-of-magnitude constraints from current data, showing that |ϵosc| ≲ O(10−2) forω ≃ 13 implies |f resNL | ≲ O(0.1–1). The model is falsifiable via correlated log-periodic features in thepower spectrum and bispectrum with a fixed frequency.