Inflation with an extra light scalar field after Planck
  Bayesian inference techniques are used to investigate situations where an
additional light scalar field is present during inflation and reheating. This
includes (but is not limited to) curvaton-type models. We design a numerical
pipeline where $\simeq 200$ inflaton setups $\times\, 10$ reheating scenarios
$= 2000$ models are implemented and we present the results for a few
prototypical potentials. We find that single-field models are remarkably robust
under the introduction of light scalar degrees of freedom. Models that are
ruled out at the single-field level are not improved in general, because good
values of the spectral index and the tensor-to-scalar ratio can only be
obtained for very fine-tuned values of the extra field parameters and/or when
large non-Gaussianities are produced. The only exception is quartic large-field
inflation, so that the best models after Planck are of two kinds: plateau
potentials, regardless of whether an extra field is added or not, and quartic
large-field inflation with an extra light scalar field, in some specific
reheating scenarios. Using Bayesian complexity, we also find that more
parameters are constrained for the models we study than for their single-field
versions. This is because the added parameters not only contribute to the
reheating kinematics but also to the cosmological perturbations themselves, to
which the added field contributes. The interplay between these two effects lead
to a suppression of degeneracies that is responsible for having more
constrained parameters.
