  We consider the computation of the entanglement entropy in curved backgrounds
with event horizons. We use a Hamiltonian approach to the problem and perform
numerical computations on a spherical lattice of spacing $a$. We study the
cosmological case and make explicit computations for the
Friedmann-Robertson-Walker universe. Our results for a massless, minimally
coupled scalar field can be summarized by $S_{ent}=0.30 r_H^2/a^2$,which
resembles the flat space formula, although here the horizon radius, $r_H$, is
time-dependent.
