  We construct large families of initial data sets for the vacuum Einstein
equations with positive cosmological constant which contain exactly Delaunay
ends; these are non-trivial initial data sets which coincide with those for the
Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the
purely Riemannian geometric point of view, this produces complete, constant
positive scalar curvature metrics with exact Delaunay ends which are not
globally Delaunay. The ends can be used to construct new compact initial data
sets via gluing constructions. The construction provided applies to more
general situations where the asymptotic geometry may have non-spherical
cross-sections consisting of Einstein metrics with positive scalar curvature.
