  In spacetime dimensions $n+1\geq 4$, we show the existence of solutions of
the Einstein vacuum equations which describe asymptotically de Sitter
spacetimes with prescribed smooth data at the conformal boundary. This provides
a short alternative proof of a special case of a result by Shlapentokh-Rothman
and Rodnianski, and generalizes earlier results by Friedrich and Anderson to
all dimensions.
