Infinite violation of Bell inequalities in inflation

Understand

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.