Decoherence of Cosmological Perturbations from Boundary Terms and the Non-Classicality of Gravity

Abstract

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 $⟨{\zeta }^n⟩$, 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 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 $\zeta$. Our calculation also indicates that density fluctuation $\delta \rho$ better preserves quantum information than $\zeta$ for the purpose of constructing cosmological Bell-like experiments.

v3: 34 pages, 3 figures; typos corrected, references and figure added. Revised the part of UV and IR divergences. Match the JHEP version

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