Decoherence and entropy of primordial fluctuations. I: Formalism and interpretation

TL;DR

This paper introduces an operational method to define the entropy of cosmological perturbations, linking quantum-to-classical transition to mode entanglement and separability, with implications for inflationary models.

Contribution

It presents a gauge-invariant, unambiguous entropy definition based on Green function truncation, and analyzes the quantum-to-classical transition via mode entanglement and separability.

Findings

Entropy is well-defined despite gauge invariance and renormalization.

Quantum-to-classical transition relates to mode entanglement and separability.

Reduced density matrices can be expressed as mixtures of less constrained squeezed states.

Abstract

We propose an operational definition of the entropy of cosmological perturbations based on a truncation of the hierarchy of Green functions. The value of the entropy is unambiguous despite gauge invariance and the renormalization procedure. At the first level of truncation, the reduced density matrices are Gaussian and the entropy is the only intrinsic quantity. In this case, the quantum-to-classical transition concerns the entanglement of modes of opposite wave-vectors, and the threshold of classicality is that of separability. The relations to other criteria of classicality are established. We explain why, during inflation, most of these criteria are not intrinsic. We complete our analysis by showing that all reduced density matrices can be written as statistical mixtures of minimal states, the squeezed properties of which are less constrained as the entropy increases. Pointer states therefore appear not to be relevant to the discussion. The entropy is calculated for various models in paper II.