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arXiv · 2306.15326

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

Artur Alho·Claes Uggla
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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.

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Artur Alho, Claes Uggla. 2023-06-27. Quintessential $\alpha$-attractor inflation: A dynamical systems analysis. https://arxiv.org/abs/2306.15326

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