Generalized $\alpha$-attractor models from elementary hyperbolic surfaces

Abstract

We consider generalized $\alpha$-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincaré disk $\mathbb{D}$, such surfaces include the hyperbolic punctured disk ${\mathbb{D}}^{\ast }$ and the hyperbolic annuli $\mathbb{A}(R)$ of modulus $\mu =2\log R>0$. For each elementary surface, we discuss its decomposition into canonical end regions and give an explicit construction of the embedding into the Kerekjarto-Stoilow compactification (which in all cases is the unit sphere), showing how this embedding allows for a universal treatment of globally well-behaved scalar potentials upon expanding their extension in real spherical harmonics. For certain simple but natural choices of extended potentials, we compute scalar field trajectories by projecting numerical solutions of the lifted equations of motion from the Poincaré half-plane through the uniformization map, thus illustrating the rich cosmological dynamics of such models.

41 pages

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Cited by in corpus (10)

• On Primordial Black Holes from Rapid Turns in Two-field Models
• Dark Energy from Inspiraling in Field Space
• Generalized two-field $\alpha$-attractor models from geometrically finite hyperbolic surfaces
• Two-field Cosmological $\alpha$-attractors with Noether Symmetry
• Dynamical consistency conditions for rapid turn inflation
• Hidden symmetries of two-field cosmological models
• Generalized two-field $\alpha$-attractors from the hyperbolic triply-punctured sphere
• The infrared behavior of tame two-field cosmological models
• Dynamical renormalization and universality in classical multifield cosmological models
• Noether Symmetries of Two-Field Cosmological Models