  In a QFT on de Sitter background, one can study correlators between fields
pushed to the future and past horizons of a comoving observer. This is a neat
probe of the physics in the observer's causal diamond (known as the static
patch). We use this observable to give a generalization of the quasinormal
spectrum in interacting theories, and to connect it to the spectral density
that appears in the K\"all\'en-Lehmann expansion of dS correlators. We also
introduce a finite-temperature effective field theory consisting of free bulk
fields coupled to a boundary. In matching it to the low frequency expansion of
correlators, we find positivity constraints on the EFT parameters following
from unitarity.
