What Planck does not tell us about inflation
  Planck data has not found the 'smoking gun' of non-Gaussianity that would
have necessitated consideration of inflationary models beyond the simplest
canonical single field scenarios. This raises the important question of what
these results do imply for more general models, and in particular, multi-field
inflation. In this paper we revisit four ways in which two-field scenarios can
behave differently from single field models; two-field slow-roll dynamics,
curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and
modulated reheating. We study the constraints that Planck data puts on these
classes of behaviour, focusing on the latter two which have been least studied
in the recent literature. We show that these latter classes are almost
equivalent, and extend their previous analyses by accounting for arbitrary
evolution of the isocurvature mode which, in particular, places important
limits on the Gaussian curvature of the reheating hypersurface. In general,
however, we find that Planck bispectrum results only constrain certain regions
of parameter space, leading us to conclude that inflation sourced by more than
one scalar field remains an important possibility.
