Inflationary $\alpha$-attractor cosmology: A global dynamical systems perspective

Abstract

We study flat FLRW $\alpha$-attractor $\mathrm{E}$- and $\mathrm{T}$-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of $e$-folds, is associated with a solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this `inflationary attractor solution.' A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.

15 pages, 11 figures. Matches published version

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• Cosmological dynamics of the general non-canonical scalar field models
• Enhanced primordial gravitational waves from a stiff post-inflationary era due to an oscillating inflaton
• T-Model Inflation and Bouncing Cosmology
• Generalized Scalar Field Cosmologies: A Global Dynamical Systems Formulation
• Non-oscillating Early Dark Energy and Quintessence from Alpha-Attractors
• Global dynamics of Yang-Mills field and perfect-fluid Robertson-Walker cosmologies
• Separatrices in the Hamilton-Jacobi Formalism of Inflaton Models
• Global Portraits of Nonminimal Inflation: Metric and Palatini
• Dynamical systems in perturbative scalar field cosmology
• Cosmological global dynamical systems analysis
• Global portraits of nonminimal inflation
• Global Portraits of Inflation in Nonsingular Variables
• Global portraits of nonminimal teleparallel inflation
• Adaptive asymptotic solutions of inflationary models in the Hamilton-Jacobi formalism: Application to T-models
• A novel way of constraining the $\alpha$-attractor chaotic inflation through Planck data