  We note that the decoherence of inflationary curvature perturbation $\zeta$
is dominated by a boundary term of the gravity action. Although this boundary
term cannot affect cosmological correlators $\left\langle \zeta^n
\right\rangle$, it induces much faster decoherence for $\zeta$ than that of
previous calculations. The gravitational origin of inflationary decoherence
sheds light on the quantum (or non-classical) nature of gravity. By comparing
with a Schr\"odinger-Newton toy model of classical gravity, we show that
gravity theories of classical or quantum origins can be distinguished by
comparing their different impacts on decoherence rate of $\zeta$. Our
calculation also indicates that density fluctuation $\delta\rho$ better
preserves quantum information than $\zeta$ for the purpose of constructing
cosmological Bell-like experiments.
