The momentum-dependent effective sound speed and multi-field inflation

For any physical system satisfying the Einstein's equations the comoving curvature perturbations satisfy an equation involving the momentum-dependent effective sound speed (MESS), valid for any system with a well defined energy-stress tensor (EST), including multi-fields models of inflation. While the power spectrum of adiabatic perturbations may generically receive contributions from many independent quantum degrees of freedom present in these models, there is often a single mode that dominates adiabatic perturbations of a given wavelength and evolves independently of other modes, with evolution entirely described by MESS. We study a number of two-field models with a kinetic coupling between the fields, identifying this single effective mode and showing that MESS fully accounts for the predictions for the power spectrum of adiabatic perturbations. Our results show that MESS is a conventient scheme for describing all inflationary models that admit a single-field effective theory, including the effects of entropy pertubations present in multi-fields systems, which are not included in the effective theory of inflation.