Decoherence of Cosmological Perturbations from Boundary Terms and the Non-Classicality of Gravity
We note that the decoherence of inflationary curvature perturbation $ζ$ is dominated by a boundary term of the gravity action. Although this boundary term cannot affect cosmological correlators $\left\langle ζ^n \right\rangle$, it induces much faster decoherence for $ζ$ 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 Schrödinger-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 $ζ$. Our calculation also indicates that density fluctuation $δρ$ better preserves quantum information than $ζ$ for the purpose of constructing cosmological Bell-like experiments.