Superhorizon entanglement entropy from particle decay in inflation

Abstract

In inflationary cosmology all particle states decay as a consequence of the lack of kinematic thresholds. The decay of an initial single particle state yields an entangled quantum state of the product particles. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the decay of a light scalar field with mass M ≪ H with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in Δ = M 2 /3H 2 and we obtain the quantum state in an expansion in Δ. To leading order the pure state density matrix describing the decay of a particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing entanglement between superhorizon and subhorizon fluctuations and correlations across the horizon. Tracing over the superhorizon degrees of freedom yields a mixed state density matrix from which we obtain the entanglement entropy. Asymptotically this entropy grows with the physical volume as a consequence of more modes of the decay products crossing the Hubble radius. A generalization to localized wave packets is provided. The cascade decay of single particle states into many particle states is discussed. We conjecture on possible impact of these results on non-gaussianity and on the "low multipole anomalies" of the CMB. © 2014 The Author(s).