Quintessential $\alpha$-attractor inflation: A dynamical systems analysis

TL;DR

This paper reformulates quintessential α-attractor inflation models into a dynamical system framework, providing a comprehensive analysis of solution space, attractor solutions, and a new method for initial data selection.

Contribution

It introduces a regular dynamical system approach for these models, linking inflationary and quintessence attractors, and proposes a novel systematic initial data method based on dynamical systems properties.

Findings

Inflationary attractor is the unstable center manifold of a de Sitter fixed point.

Connections between slow-roll and dynamical systems approximations are established.

A new method for initial data selection exploits fixed point structures.

Abstract

The equations for quintessential $\alpha$-attractor inflation with a single scalar field, radiation and matter in a spatially flat FLRW spacetime are recast into a regular dynamical system on a compact state space. This enables a complete description of the solution space of these models. The inflationary attractor solution is shown to correspond to the unstable center manifold of a de Sitter fixed point, and we describe connections between slow-roll and dynamical systems approximations for this solution, including Pad\'e approximants. We also introduce a new method for systematically obtaining initial data for quintessence evolution by using dynamical systems properties; in particular, this method exploits that there exists a radiation dominated line of fixed points with an unstable quintessence attractor submanifold, which plays a role that is reminiscent of that of the inflationary attractor solution for inflation.