Abstract. The main objective of the cosmological bootstrap program is to derive cosmological correlators on the boundary of a quasi-dS space from basic principles such as unitarity and analyticity. In this talk we show how to extend the reach of this program by going beyond the dS invariant setup: we adapt the bootstrap methods to situations where the inflation field has a reduced speed of sound and has sizeable couplings to additional massive fields during inflation. We leverage the cosmological optical theorem and cosmological boundary equations to find analytical expressions for sample contributions to the two- and three-point functions of the inflation field as a result of the exchange of a massive scalar. We find new shapes of non-gaussianity with novel oscillatory features in the mildly squeezed limit, which are not present in the standard cosmological collider physics signal.