Decoherence of cosmological perturbations from boundary terms and the non-classicality of gravity

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