Bootstrapping Multi-Field Inflation: non-Gaussianities from light scalars revisited

Abstract: 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.