# Infinite violation of Bell inequalities in inflation

## TL;DR

This paper investigates Bell inequality violations in inflationary quantum states, revealing that certain non-Bunch-Davies states can exponentially violate Bell inequalities with increasing modes, suggesting quantum origins in cosmological data.

## Contribution

It demonstrates that non-Bunch-Davies vacuum states can exponentially violate Bell inequalities with more modes, unlike Bunch-Davies states which do not increase violation.

## Key findings

- Bunch-Davies vacuum maximally violates Bell inequalities.
- Violation does not grow with modes in Bunch-Davies state.
- Non-Bunch-Davies state shows exponential violation growth.

## Abstract

We study the violation of Bell-Mermin-Klyshko (BMK) inequalities in initial quantum states of scalar fields in inflation. We show that the Bell inequality is maximally violated by the Bunch-Davies vacuum which is a two-mode squeezed state of a scalar field. However, we find that the violation of the BMK inequalities does not increase with the number of modes to measure. We then consider a non-Bunch-Davies vacuum expressed by a four-mode squeezed state of two scalar fields. Remarkably, we find that the violation of the BMK inequalities increases exponentially with the number of modes to measure. This indicates that some evidence that our universe has a quantum mechanical origin may survive in CMB data even if quantum entanglement decays exponentially afterward due to decoherence.