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We propose a class of two-field cosmological models derived from gravitycoupled to non-linear sigma models whose target space is a non-compact andgeometrically-finite hyperbolic surface, which provide a wide generalization ofso-called $\alpha$-attractor models and can be studied using uniformizationtheory. We illustrate cosmological dynamics in such models for the case of thehyperbolic triply-punctured sphere.

Two-field cosmological models and the uniformization theorem