  Cosmological correlation functions contain valuable information about the
primordial Universe, with possible signatures of new massive particles at very
high energies. Recent developments, including the cosmological bootstrap, bring
new perspectives and powerful tools to study these observables. In this paper,
we systematically classify inflationary three-point correlators of scalar
perturbations using the bootstrap method. For the first time, we derive a
complete set of single-exchange cosmological collider bispectra with new shapes
and potentially detectable signals. Specifically, we focus on the primordial
scalar bispectra generated from the exchange of massive particles with all
possible boost-breaking interactions during inflation. We introduce three-point
"seed" functions, from which we bootstrap the inflationary bispectra of scalar
and spinning exchanges using weight-shifting and spin-raising operators. The
computation of the seed function requires solving an ordinary differential
equation in comoving momenta, a boundary version of the equation of motion
satisfied by a propagator that linearly mixes a massive particle with the
external light scalars. The resulting correlators are presented in analytic
form, for any kinematics. These shapes are of interest for near-future
cosmological surveys, as the primordial non-Gaussianity in boost-breaking
theories can be large. We also identify new features in these shapes, which are
phenomenologically distinct from the de Sitter invariant cases. For example,
the oscillatory shapes around the squeezed limit have different phases.
Furthermore, when the massive particle has much lower speed of sound than the
inflaton, oscillatory features appear around the equilateral configuration.
