Metric perturbations in two-field inflation

TL;DR

This work analyzes metric perturbations in two-field inflation, demonstrating that entropy modes can break the usual conservation of the super-horizon curvature perturbation $ζ$. It develops both the standard linear perturbation and Sasaki–Stewart delta-N formalisms, showing their equivalence for calculating end-of-inflation perturbations in separable-potential models under slow-roll. The authors derive explicit scalar and tensor spectra, establish an inequality $R≤6|n_g|$ between tensor-to-scalar ratio and gravitational-wave tilt (saturating only when perturbations are adiabatic), and explore special cases such as Brans–Dicke and minimally coupled scenarios. The results highlight how multi-field dynamics modify single-field predictions and emphasize the need to account for reheating when connecting inflationary perturbations to late-time observables.

Abstract

We study the metric perturbations produced during inflation in models with two scalar fields evolving simultaneously. In particular, we emphasize how the large-scale curvature perturbation $ζ$ on fixed energy density hypersurfaces may not be conserved in general for multiple field inflation due to the presence of entropy as well as adiabatic fluctuations. We show that the usual method of solving the linearized perturbation equations is equivalent to the recently proposed analysis of Sasaki and Stewart in terms of the perturbed expansion along neighboring trajectories in field-space. In the case of a separable potential it is possible to compute in the slow-roll approximation the spectrum of density perturbations and gravitational waves at the end of inflation. In general there is an inequality between the ratio of tensor to scalar perturbations and the tilt of the gravitational wave spectrum, which becomes an equality when only adiabatic perturbations are possible and $ζ$ is conserved.