This paper introduces inflation as a dynamical filter acting on the space of Hamiltonians, rather than merely on fields evolving within a fixed background. The stability functional SH is defined from the influence functional on a quasi–de Sitter background, quantifying how robustly a Hamiltonian maintains controlled, semiclassical evolution under repeated coarse–smooth filtering. The ensemble‑flow equation N PH = SH PH describes how inflation exponentially reweights Hamiltonians toward local maxima of SH. Lorentz‑invariant dispersion relations, gauge‑symmetric Hamiltonians, and fixed‑point coupling ratios emerge as conditional structural attractors when they correspond to stability maxima within their Hamiltonian families. Explicit computations for Lorentz‑violating and interacting scalar theories demonstrate that the stability functional is physically meaningful and technically tractable. A key quantitative prediction is ensemble narrowing N (N a) ^-1/2, leading to falsifiable bounds on sound speed deviations |cₛ - 1| and equilateral non‑Gaussianity |f₍₋^equil|. Backreaction is shown to enter at higher order, ensuring the mechanism is stable under gravitational feedback. This paper is the fourth in a series developing the ensemble‑flow mechanism for Hamiltonian selection during inflation. Subsequent work will extend the stability functional to fermions, non‑Abelian gauge fields, and full gravitational backreaction.
Robert Clark (Thu,) studied this question.