Superhorizon entanglement entropy from particle decay in inflation

TL;DR

This paper studies how particle decay during inflation leads to superhorizon entanglement entropy, revealing quantum correlations across the horizon and their growth with volume, with potential implications for cosmological observations.

Contribution

It extends a unitary quantum field theoretical method to analyze superhorizon entanglement entropy from particle decay in inflationary cosmology, including infrared effects and generalizations to wave packets.

Findings

Entanglement between superhorizon and subhorizon fluctuations due to particle decay.

Entanglement entropy grows with physical volume as more modes cross the horizon.

Decay processes may influence non-Gaussianity and CMB anomalies.

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 \emph{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 $M\ll H$ with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in $\Delta=M^2/3H^2$ and we obtain the quantum state in an expansion in $\Delta$. To leading order in $\Delta$ the pure state density matrix describing the decay of a particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing \emph{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 \emph{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 \emph{possible} impact of these results on non-gaussianity and on the ``low multipole anomalies'' of the CMB.