  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 two simple and calculable classes of examples:
conformal field theories (CFTs), and large-N CFTs deformed by relevant
time-dependent double-trace operators. Together these two classes of examples
exhibit a wide range of scalings and shapes of the bispectrum, including nearly
equilateral, orthogonal and local non-Gaussianity in different regimes. Along
the way, we compare and contrast the shape and amplitude with previous results
on weakly coupled fields coupled to inflation. 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.
