In the '80s, Klainerman and Sarnak obtained explicit solutions for the wave equation in homogeneous and isotropic universes filled with dust. We generalize their work to several Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes of hyperbolic, flat and spherical spatial curvature and discuss decay rates and the validity of the Huygens principle. The method consists in finding differential operators that map solutions of the wave equation in these FLRW spacetimes to solutions of the conformally invariant wave equation in simpler, ultra-static spacetimes, for which spherical mean formulas are available. Conjectures for the general decay rates in flat and hyperbolic FLRW spacetimes, inspired by numerical results, will also be discussed. The talk is based on joint work with J. Natário and A. Vañó-Viñuales.