Minimal Conditions for Hamiltonian‑Sector Decoherence in de Sitter Space

This work develops a minimal and model‑agnostic framework in which decoherence between inequivalent Hamiltonian sectors leads to dynamically autonomous branches characterized by definite couplings in a de Sitter background. Coupling constants are promoted to operators acting on an auxiliary “law Hilbert space,” and sector‑dependent interactions with a massless scalar environment generate a decoherence functional that grows logarithmically with the scale factor. An explicit influence‑functional example is provided, along with conditions under which Hamiltonian sectors become pointer states during inflation. The framework isolates the universal features of Hamiltonian‑sector decoherence while remaining agnostic about sector structure, dimensionality, or UV origin.