  The existence of quasinormal modes (QNMs) for waves propagating on pure de
Sitter space has been called into question in several works. We definitively
prove the existence of quasinormal modes for massless and massive scalar fields
in all dimensions and for all scalar field masses, and present a simple method
for the explicit calculation of QNMs and the corresponding mode solutions. By
passing to coordinates which are regular at the cosmological horizon, we
demonstrate that certain QNMs only appear in the QNM expansion of the field
when the initial data do not vanish near the cosmological horizon. The key
objects in the argument are dual resonant states. These are distributional mode
solutions of the adjoint field equation satisfying a generalized incoming
condition at the horizon, and they characterize the amplitudes with which QNMs
contribute to the QNM expansion of the field.
