On the viability of m**2 phi**2 and natural inflation
  In the context of single field inflation, models with a quadratic potential
and models with a natural potential with subplanckian decay constant are in
tension with the Planck data. We show that, when embedded in a two-field model
with an additional super massive field, they can become consistent with
observations. Our results follow if the inflaton is the phase of a complex
field (or an angular variable) protected by a mildly broken U(1) symmetry, and
the radial component, whose mass is much greater than the Hubble scale, is
stabilized at subplanckian values. The presence of the super massive field,
besides modifying the effective single field potential, causes a reduction in
the speed of sound of the inflaton fluctuations, which drives the prediction
for the primordial spectrum towards the allowed experimental values. We discuss
these effects also for the linear potential, and show that this model increases
its agreement with data as well
