Superhorizon entanglement entropy from particle decay in inflation
  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.
