Coupling structure of multi-field primordial perturbations
  We investigate the coupling relations among perturbations in general
multi-field models. We derived the equations of motion for both background and
perturbations in a general basis. Within this formalism, we revisit the
construction of kinematic orthogonal normal vectors using the successive time
derivatives of the background field velocity. We show that the coupling
relations among modes in this kinematic basis can be reduced, by employing the
background equations of motion for the scalar fields and their high order time
derivatives. There are two typical features in the field space: inflationary
trajectory and geometry of the potential. Correspondingly, the couplings among
modes fall into two categories: one is controlled only by the kinematic
quantities, the other involves high order derivatives of the potential.
Remarkably, the couplings of the first category, i.e. controlled by the
kinematic quantities only, show a "chain" structure. That is, each mode is only
coupled to its two neighbour modes.
