Delta-N formalism for the evolution of the curvature perturbations in generalized multi-field inflation

The δN formalism is considered to calculate the evolution of the curvature perturbation in generalized multi-field inflation models. The result is consistent with the usual calculation of the standard kinetic term. For the calculation of the generalized kinetic term, we improved the definition of the adiabatic field. Our calculation improves the usual calculation of R˙ based on the field equations and the perturbations, giving a very simple and intuitive argument for the evolution equations in terms of the perturbations of the inflaton velocity. Significance of non-equilibrium corrections are also discussed, which is caused by the small-scale (decaying) inhomogeneities. This formalism based on the modulated inflation scenario (i.e., calculation based on the perturbations related to the inflaton velocity) provides a powerful tool for investigating the signature of moduli that may appear in string theory.