The Importance of Slow-roll Corrections During Multi-field Inflation
  We re-examine the importance of slow-roll corrections during the evolution of
cosmological perturbations in models of multi-field inflation. We find that in
many instances the presence of light degrees of freedom leads to situations in
which next to leading order slow-roll corrections become significant. Examples
where we expect such corrections to be crucial include models in which modes
exit the Hubble radius while the inflationary trajectory undergoes an abrupt
turn in field space, or during a phase transition. We illustrate this with two
examples -- hybrid inflation and double quadratic inflation. Utilizing both
analytic estimates and full numerical results, we find that corrections can be
as large as 20%. Our results have implications for many existing models in the
literature, as these corrections must be included to obtain accurate
observational predictions -- particularly given the level of accuracy expected
from CMB experiments such as Planck
