  It is well-known that the primordial scalar curvature and tensor
perturbations, $\zeta$ and $\gamma_{ij}$, are conserved on super-horizon scales
in minimal inflation models. However, their wave functional has a rapidly
oscillating phase which is slow-roll unsuppressed, as can be seen either from
boundary (total-derivative) terms of cosmological perturbations, or the WKB
approximation of the Wheeler-DeWitt equation. Such an oscillatory phase
involves gravitational non-linearity between scalar and tensor perturbations.
By tracing out unobserved modes, the oscillatory phase causes faster
decoherence of primordial gravitons compared to those by bulk interactions. Our
results put a stronger lower bound of decoherence effect to the recent
proposals probing squeezed primordial gravitons.
