Statistical Bounds on CMB Bell Violation

Inspired the low $\mathrm{\ell }$ cosmic variance we present a study on the statistical variance expected in observing Bell’s inequality violation by primordial quantum states violation. We consider the statistical variance inherent to three sets of pseudo-spin operators used to construct Bell’s inequality. We find that for a highly squeezed state, such as the relevant CMB states, the statistical variation will vanish and does not contribute to theoretical uncertainties.