Violation of Bell inequality from a squeezed coherent state of inflationary perturbations

TL;DR

This paper explores how primordial quantum states during inflation, modeled as coherent states evolving into squeezed states, can violate Bell inequalities, revealing quantum correlations in early universe perturbations.

Contribution

It introduces an analytical framework for Bell inequality violation from coherent initial states in inflationary cosmology, extending previous vacuum-based analyses.

Findings

Bell operator expectation value deviates initially but saturates over time.

Larger coherent state parameters lead to faster saturation of Bell violation.

The saturation value matches the vacuum case asymptotically.

Abstract

We investigate the quantum nature of primordial perturbations by studying the violation of Bell inequality when the initial state is taken to be a coherent state rather than the usual Bunch-Davies vacuum. As inflation progresses, the coherent state evolves into a squeezed coherent state, and we derive an analytical expression for the expectation value of the Bell operator constructed from pseudo-spin operators. Our analysis shows that although the expectation value of the Bell operator initially deviates from the vacuum case, it asymptotically saturates to the same value. Notably, this saturation occurs more rapidly for non-zero coherent state parameters, indicating that a larger one-point correlation function accelerates the approach to maximal Bell inequality violation.