  We calculate Sorkin's manifestly covariant entanglement entropy $\mathcal{S}$
for a massive and massless minimally coupled free Gaussian scalar field for the
de Sitter horizon and Schwarzschild de Sitter horizons respectively in $d > 2$.
In de Sitter spacetime we restrict the Bunch-Davies vacuum in the conformal
patch to the static patch to obtain a mixed state. The finiteness of the
spatial $\mathcal{L}^2$ norm in the static patch implies that $\mathcal{S}$ is
well defined for each mode. We find that $\mathcal{S}$ for this mixed state is
independent of the effective mass of the scalar field, and matches that of
Higuchi and Yamamoto, where, a spatial density matrix was used to calculate the
horizon entanglement entropy. Using a cut-off in the angular modes we show that
$\mathcal{S} \propto A_{c}$, where $A_c$ is the area of the de Sitter
cosmological horizon. Our analysis can be carried over to the black hole and
cosmological horizon in Schwarzschild de Sitter spacetime, which also has
finite spatial $\mathcal{L}^2$ norm in the static regions. Although the
explicit form of the modes is not known in this case, we use appropriate
boundary conditions for a massless minimally coupled scalar field to find the
mode-wise $\mathcal{S}_{b,c}$, where $b,c$ denote the black hole and de Sitter
cosmological horizons, respectively. As in the de Sitter calculation we see
that $\mathcal{S}_{b,c} \propto A_{b,c}$ after taking a cut-off in the angular
modes.
