  Phenomenological studies of cosmological collider physics in recent years
have identified many 1-loop inflation correlators as leading channels for
discovering heavy new particles around or above the inflation scale. However,
complete analytical results for these massive 1-loop correlators are currently
unavailable. In this work, we embark on a program of bootstrapping inflation
correlators with massive exchanges at 1-loop order, with the input of
tree-level inflation correlators and the techniques of spectral decomposition
in dS. As a first step, we present for the first time the complete and
analytical results for a class of 4-point and 3-point inflation correlators
mediated by massive scalar fields at the 1-loop order. Using the full result,
we provide simple and reliable analytical approximations for the signals and
the background in the squeezed limit. We also identify configurations of the
scalar trispectrum where the oscillatory signal from the loop is dominant over
the background.
