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

Understand

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.