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 $\hat{I}\P$ is coupled to an isocurvature perturbation $\ddot{I}ƒ$ of entropy mass $\hat{I}¼$. The solutions are valid for arbitrary values of $\hat{I}¼$ and the dimensionless interaction strength $\hat{I}»$, within a quasi-de Sitter background. They therefore provide analytic control over the strong mixing regime in which $\hat{I}\P$ 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.

5 pages + references, 2 figures. v2: Introduced new notation for the canonically normalized curvature perturbation and the Bogoliubov coefficients, and a new definition of the f_M solution