  We show that, for general static or axisymmetric stationary spacetimes, a
cosmological Killing horizon exists only if $R_{ab}n^{a}n^{b}< 0$ for a
hypersurface orthogonal timelike $n^{a}$, at least over some portion of the
region of interest of the manifold. This implies violation of the strong energy
condition by the matter fields, the simplest example of which is a positive
cosmological constant.
