Primordial non-Gaussianities from multi-field inflation are a leading target
for cosmological observations, because of the possible large correlations
generated between long and short distances. These signatures are captured by
the local shape of the scalar bispectrum. In this paper, we revisit the
nonlinearities of the conversion process from additional light scalars into
curvature perturbations during inflation. We provide analytic templates for
correlation functions valid at any kinematical configuration, using the
cosmological bootstrap as a main computational tool. Our results include the
possibility of large breaking of boost symmetry, in the form of small speeds of
sound for both the inflaton and the mediators. We consider correlators coming
from the tree-level exchange of a massless scalar field. By introducing a
late-time cutoff, we identify that the symmetry constraints on the correlators
are modified. This leads to anomalous conformal Ward identities, and
consequently the bootstrap differential equations acquire a source term that
depends on this cutoff. The solutions to the differential equations are scalar
seed functions that incorporate these late-time growth effects. Applying
weight-shifting operators to auxiliary “seed” functions, we obtain a systematic
classification of shapes of non-Gaussianity coming from massless exchange. For
theories with de Sitter symmetry, we compare the resulting shapes with the ones
obtained via the $\delta N$ formalism, identifying missing contributions away
from the squeezed limit. For boost-breaking scenarios, we derive a novel class
of shape functions with phenomenologically distinct features. Specifically, the
new shape provides a simple extension of equilateral non-Gaussianity: the
signal peaks at a geometric configuration controlled by the ratio of the sound
speeds of the mediator and the inflaton.

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