A New delta N Formalism for Multi-Component Inflation

TL;DR

The authors extend the delta-N formalism to multi-component inflation, removing the requirement that all fields obey slow-roll at horizon crossing and formulating a general slow-roll framework centered on the relevant component. They derive a gauge-invariant $\delta N_f$ that evolves simply from sub-horizon to super-horizon scales and compute the curvature perturbation power spectrum to leading order, showing its invertibility through kernels like $s(x)$. The work provides a practical method to connect the observed curvature spectrum to the underlying multi-field inflationary dynamics and introduces an inversion procedure to reconstruct background quantities from data. This framework broadens the applicability of delta-N to realistic, multi-field scenarios and offers a path for precision cosmology in models with many scalar fields.

Abstract

The delta N formula that relates the final curvature perturbation on comoving slices to the inflaton perturbation on flat slices after horizon crossing is a powerful and intuitive tool to compute the curvature perturbation spectrum from inflation. However, it is customarily assumed further that the conventional slow-roll condition is satisfied, and satisfied by all components, during horizon crossing. In this paper, we develop a new delta N formalism for multi-component inflation that can be applied in the most general situations. This allows us to generalize the idea of general slow-roll inflation to the multi-component case, in particular only applying the general slow-roll condition to the relevant component. We compute the power spectrum of the curvature perturbation in multi-component general slow-roll inflation, and find that under quite general conditions it is invertible.