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Cosmological correlation functions contain valuable information about theprimordial Universe, with possible signatures of new massive particles at veryhigh energies. Recent developments, including the cosmological bootstrap, bringnew perspectives and powerful tools to study these observables. In this paper,we systematically classify inflationary three-point correlators of scalarperturbations using the bootstrap method. For the first time, we derive acomplete set of single-exchange cosmological collider bispectra with new shapesand potentially detectable signals. Specifically, we focus on the primordialscalar bispectra generated from the exchange of massive particles with allpossible boost-breaking interactions during inflation. We introduce three-point"seed" functions, from which we bootstrap the inflationary bispectra of scalarand spinning exchanges using weight-shifting and spin-raising operators. Thecomputation of the seed function requires solving an ordinary differentialequation in comoving momenta, a boundary version of the equation of motionsatisfied by a propagator that linearly mixes a massive particle with theexternal light scalars. The resulting correlators are presented in analyticform, for any kinematics. These shapes are of interest for near-futurecosmological surveys, as the primordial non-Gaussianity in boost-breakingtheories can be large. We also identify new features in these shapes, which arephenomenologically 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 theinflaton, oscillatory features appear around the equilateral configuration.

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