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We derive the canonically normalized modes of a two-field inflationary system with arbitrary constant quadratic mixing and unequal sound speeds $c_φ$ and $c_σ$ for the curvature and isocurvature perturbations, respectively. A Laplace representation reduces the coupled dynamics to a second-order Heun equation and gives the exact late-time curvature power spectrum for arbitrary values of the mixing parameter and entropy mass.
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