We study the gravitational production of super-Hubble-mass dark matter in the very early universe. We first review the simplest scenario where dark matter is produced mainly during slow roll inflation. Then we move on to consider the cases where dark matter is produced during the transition period between inflation and the subsequent cosmological evolution. The limits of smooth and sudden transitions are studied, respectively. The relic abundances and the cosmological collider signals are calculated.

We analyze gravitational particle production assisted by chemical potential. By utilizing the uniformly smoothed Stokes-line method and Borel summation, we gain insight into the fine-grained history of enhanced particle production. Analytic/semi-analytic formulae describing the production amount, time and width are obtained for both spin-1 and spin-1/2 particles in various FRW spacetimes. Our work also serves as a concrete demonstration of the uniformly smoothed Stokes-line method applied to cosmology.

We study the decoherence of massive fields during inflation based on the Zurek's density matrix approach. With the cubic interaction between inflaton and massive fields, the reduced density matrix for the massive fields can be calculated in the Schrödinger picture which is related to the variance of the non-Gaussian exponent in the wave functional. The decoherence rate is computed in the one-loop form from functional integration. For heavy fields with m O(H), quantum fluctuations will easily stay in the quantum state and decoherence is unlikely. While for light fields with mass smaller than O(H), quantum fluctuations are easily decohered within 5 ∼ 10 e-folds after Hubble crossing. Thus heavy fields can play a key role in studying problems involving inflationary quantum information.

It is well-known that the primordial scalar curvature and tensor perturbations, ζ and γij, are conserved on super-horizon scales in minimal inflation models. However, their wave functional has a rapidly oscillating phase which is slow-roll unsuppressed, as can be seen either from boundary (total-derivative) terms of cosmological perturbations, or the WKB approximation of the Wheeler-DeWitt equation. Such an oscillatory phase involves gravitational non-linearity between scalar and tensor perturbations. By tracing out unobserved modes, the oscillatory phase causes faster decoherence of primordial gravitons compared to those by bulk interactions. Our results put a stronger lower bound of decoherence effect to the recent proposals probing squeezed primordial gravitons.

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 〈ζn〉, 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.

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

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