We analyze the signatures of inflationary models that are coupled to strongly interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze a simple and calculable class of examples: conformal field theories (CFTs). They exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to 1000 times the inflationary Hubble scale.

Stanford University and CERN