Pushing the Primordial Frontier: Exact Linear Solutions in Multifield Inflation

We present exact analytic solutions for the linear dynamics of a two-field inflationary system in which the primordial curvature perturbation $\zeta$ is coupled to an isocurvature perturbation $\sigma$ of entropy mass $\mu$. The solutions are valid for arbitrary values of $\mu$ and the dimensionless interaction strength $\lambda$, within a quasi-de Sitter background. They therefore provide analytic control over the strong mixing regime in which $\zeta$ 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 mixed, strongly mixed, 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.