Two-field cosmological models and the uniformization theorem

TL;DR

This paper introduces a new class of two-field cosmological models based on hyperbolic surfaces, extending $l$-attractor models, and analyzes their dynamics using uniformization theory.

Contribution

It develops a novel framework for two-field cosmological models using hyperbolic geometry and uniformization theory, broadening the scope of existing $l$-attractor models.

Findings

Models based on hyperbolic triply-punctured sphere exhibit rich cosmological dynamics.

Uniformization theory provides a powerful tool for analyzing these models.

The framework generalizes previous $l$-attractor models to more complex geometries.

Abstract

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