Hidden supersymmetry of domain walls and cosmologies

We show that all domain-wall solutions of gravity coupled to scalar fields for which the worldvolume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential determined by the solution. By analytic continuation, all flat or closed FLRW cosmologies are shown to satisfy similar first-order equations arising from the existence of ``pseudo-Killing'' spinors.