Pushing the Primordial Frontier: Exact Linear Solutions in Multifield Inflation

Abstract

We present exact analytic solutions for the linear dynamics of a two-field inflationary system in which the primordial curvature perturbation $ζ$ is coupled to an isocurvature perturbation $σ$ of entropy mass $μ$. The solutions are valid for arbitrary values of $μ$ and the dimensionless interaction strength $λ$, within a quasi-de Sitter background. They therefore provide analytic control over the strongly coupled regime in which $ζ$ interacts with light isocurvature fields, commonly associated with rapid-turn inflation. As a first application, we derive the amplitude of the primordial power spectrum in closed form, obtaining an expression that interpolates between the weakly coupled, strongly coupled, light-field, and heavy-field regimes. These results open the way to analytic studies of multifield observables beyond the power spectrum, including non-Gaussianity, particle production, and loop corrections.