Influence of heavy modes on perturbations in multiple field inflation

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.