Infinite violation of Bell inequalities in inflation
In this talk, I will explain how to quantify the quantumness of initial quantum states of scalar fields in inflation. It is shown that the Bell inequality is maximally violated by the Bunch-Davies vacuum which is a two-mode squeezed state of a scalar field. Then the analysis is extended to a non-Bunch-Davies vacuum expressed by a four-mode squeezed state of two scalar fields. Remarkably, it turns out that the violation of the Bell inequalities for this case 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.