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

Abstract

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 ζ n , 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. CONTENTS I. Introduction 3 II. Decoherence Rate with the Schrödinger wave functional 6 A. The formalism 6 B. With interacting boundary terms 8 III. Boundary Term of ζ and Decoherence 9 A. The well-defined variational principle 10 B. Decoherence rate from perturbative expansion 11 C. Decoherence rate from the Saddle-point approximation 13 D. The boundary term with the δφ-gauge and the choice of boundary 14 IV. The IR and UV Divergences of Decoherence Rate 17