Quantum-to-classical transition with nonlinear dynamics and open-system effects

Establish when curvature perturbations become effectively classical beyond linear theory while including nonlinear dynamics, mode couplings, gravitational self-interactions, interactions with other fields, entanglement across spatial regions, and the associated open-quantum-system decoherence.

Background

The analysis is restricted to linear perturbations in a closed system with a Gaussian initial state, for which the Wigner function remains positive and squeezing provides a practical classicality diagnostic. Nonlinear evolution can destroy Gaussianity and generate interference structure in the Wigner function, making the linear squeezing criterion insufficient.

The authors further note that realistic curvature perturbations cannot generally be treated as isolated systems: interactions, mode couplings, gravitational self-interactions, and spatial entanglement require an open-system treatment with decoherence. A comprehensive treatment of these effects and their implications for stochastic inflation is explicitly left unresolved.

References

Consequently, the squeezing formalism and $\mathcal{C}_k$ in Eq.~(\ref{eq:classicality_parameter}) inferred from liner dynamics becomes insufficient to determine when modes become effectively classical. In general, curvature perturbations beyond linear theory cannot be treated as an isolated system because interactions with other fields, mode couplings, gravitational self-interactions, and entanglement across spatial regions require an open quantum system description subject to decoherence. A detailed study of the quantum-to-classical transition and implications for stochastic inflation including the effects of non-linear dynamics and open-system interactions, is beyond the scope of this paper and is left for future work.

— Classical Noise in Transient USR Inflation  (2609.19478 - N. et al., 16 Sep 2026) in Section 5, Conclusion