Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion

TL;DR

This work derives the complete set of primordial curvature and isocurvature perturbations for generic two-field inflation in a slow-roll expansion, including next-to-leading order corrections and the cross-correlation at horizon exit. By rotating to a basis where perturbations are uncorrelated at Hubble exit and then to the adiabatic/isocurvature basis, the authors define a correlation angle $\Delta$ and compute horizon-exit spectra, which are evolved to late times via transfer functions $T_{RS}$ and $T_{SS}$ to yield final spectra and tilts up to second order in slow-roll. They present generalised consistency relations among scalar and tensor perturbations, plus special-case simplifications for straight trajectories, inflaton and curvaton scenarios, and symmetry-based curvature generation; they show cross-correlation can be large and strongly scale-dependent when the trajectory is curved. The framework links multi-field dynamics to observable CMB and large-scale structure signatures through the correlation angle $\Delta$ and the transfer functions, informing constraints on inflationary models and post-inflationary reheating scenarios.

Abstract

We calculate the power spectra of primordial curvature and isocurvature perturbations from a general two field inflation model at next-to-leading order correction in a slow-roll expansion. In particular we calculate the spectral indices to second order in slow-roll parameters. We show that the cross-correlation of the curvature and isocurvature perturbations at the time of Hubble-exit during inflation is non-zero at first-order in slow-roll parameters. We apply our results to different classes of inflation, including inflaton and curvaton scenarios. The spectrum of primordial gravitational waves, curvature and isocurvature perturbations obey generalised consistency relations in two-field inflation models. We give the first two consistency relations in an infinite hierarchy.