Planck-Suppressed Operators
  We show that the recent Planck limits on primordial non-Gaussianity impose
strong constraints on light hidden sector fields coupled to the inflaton via
operators suppressed by a high mass scale \Lambda. We study a simple effective
field theory in which a hidden sector field is coupled to a shift-symmetric
inflaton via arbitrary operators up to dimension five. Self-interactions in the
hidden sector lead to non-Gaussianity in the curvature perturbations. To be
consistent with the Planck limit on local non-Gaussianity, the coupling to any
hidden sector with light fields and natural cubic couplings must be suppressed
by a very high scale \Lambda > 10^5 H. Even if the hidden sector has Gaussian
correlations, nonlinearities in the mixing with the inflaton still lead to
non-Gaussian curvature perturbations. In this case, the non-Gaussianity is of
the equilateral or orthogonal type, and the Planck data requires \Lambda > 10^2
H.
