  We investigate linear cosmological perturbations in multiple field
inflationary models where some of the directions are light while others are
heavy (with respect to the Hubble parameter). By integrating out the massive
degrees of freedom, we determine the multi-dimensional effective theory for the
light degrees of freedom and give explicitly the propagation matrix that
replaces the effective sound speed of the one-dimensional case. We then examine
in detail the consequences of a sudden turn along the inflationary trajectory,
in particular the possible breakdown of the low energy effective theory in case
the heavy modes are excited. Resorting to a new basis in field space, instead
of the usual adiabatic/entropic basis, we study the evolution of the
perturbations during the turn. In particular, we compute the power spectrum and
compare with the result obtained from the low energy effective theory.
