Real-space Bell inequalities in de Sitter

TL;DR

This paper develops a formalism for Bell inequalities in real-space quantum fields, applies it to de Sitter space, and finds that quantum correlations are hidden due to effective decoherence, questioning the quantum origin of cosmological structures.

Contribution

It introduces a method to construct Bell operators for quantum fields in real space and analyzes their expectation values in de Sitter space, revealing limitations in detecting quantum correlations.

Findings

Bell inequalities are not violated in real space for de Sitter quantum fields.

Effective decoherence from tracing over other locations erases quantum features.

Quantum correlations are hidden, challenging the quantum interpretation of cosmological structures.

Abstract

Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as cosmological density fluctuations. In this work, we show how Bell operators can be constructed for quantum fields in real space, and for Gaussian states we compute their expectation value in terms of the field power spectra. We then apply our formalism to a scalar field in de-Sitter space-time. We find that, in spite of the tremendous production of entangled particles with opposite wave momenta on large scales, Bell inequalities are not violated in real space. The reason is that, when considering measurements of a field at two distinct locations in real space, one implicitly traces over the configuration of the field at every other location, leading to a mixed bipartite system. This "effective decoherence" effect is responsible for the erasure of quantum features, and casts some doubts on our ability to reveal the quantum origin of cosmological structures. We finally discuss these results in the light of quantum discord.