Cosmological Bell Tests with Decoherence Effects

TL;DR

This paper investigates how decoherence effects influence the violation of Bell inequalities in primordial cosmological fluctuations, providing a potential observational window to test their quantum origin during inflation.

Contribution

It introduces a framework incorporating decoherence effects into cosmological Bell tests, and proposes a Bell test curve to analyze quantum-to-classical transition of primordial perturbations.

Findings

Decoherence effects can restore Bell inequalities, indicating a transition from quantum to classical behavior.

A Bell test curve around 5 e-folds can be used to probe the quantum nature of primordial fluctuations.

The approach allows potential extraction of decoherence rates and interaction structures from cosmological data.

Abstract

The inflationary universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Operators involving the momenta of the fluctuations can be rewritten into pseudo-spin operators, such as the Gour-Khanna-Mann-Revzen (GKMR) pseudo-spin. Making use of these pseudo-spin operators, cosmological Bell inequalities can be formulated. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. In this work, we focus on primordial curvature perturbations. Since curvature perturbations arise from gravity, their action includes the Gibbons-Hawking-York boundary term. We clarify the role of the boundary term in selecting suitable initial conditions for linear perturbations. After that, we proceed to the interactions of cosmological perturbations, including the bulk and boundary interaction terms, which introduce decoherence effects. These decoherence effects change the expectation value of the Bell operator, and gradually restore the Bell inequality. We describe this process by a ``Bell test curve'', which offers a window around 5 e-folds for testing the quantum origin of cosmological perturbations. We also explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test curve.