  The inflationary universe creates particle pairs, which are entangled in
their momenta due to momentum conservation. Operators involving the momenta of
the fluctuations can be rewritten into pseudo-spin operators, such as the
Gour-Khanna-Mann-Revzen (GKMR) pseudo-spin. Making use of these pseudo-spin
operators, cosmological Bell inequalities can be formulated. The violation of
these Bell inequalities indicates the quantum nature of primordial
fluctuations.
  In this work, we focus on primordial curvature perturbations. Since curvature
perturbations arise from gravity, their action includes the
Gibbons-Hawking-York boundary term. We clarify the role of the boundary term in
selecting suitable initial conditions for linear perturbations.
  After that, we proceed to the interactions of cosmological perturbations,
including the bulk and boundary interaction terms, which introduce decoherence
effects. These decoherence effects change the expectation value of the Bell
operator, and gradually restore the Bell inequality. We describe this process
by a ``Bell test curve'', which offers a window around 5 e-folds for testing
the quantum origin of cosmological perturbations. We also explore the
possibility of extracting the information of the decoherence rate and the
structure of primordial interactions from the Bell test curve.
