Abstract
The equations for quintessential α-attractor inflationwith a single scalar field, radiation and matter in a spatially flatFLRW spacetime are recast into a regular dynamical system on acompact state space. This enables a complete description of thesolution space of these models. The inflationary attractor solutionis shown to correspond to the unstable center manifold of a deSitter fixed point, and we describe connections between slow-rolland dynamical systems approximations for this solution, includingPadé approximants. We also introduce a new method forsystematically obtaining initial data for quintessence evolution byusing dynamical systems properties; in particular, this method exploitsthat there exists a radiation dominated line of fixed points withan unstable quintessence attractor submanifold, which plays a rolethat is reminiscent of that of the inflationary attractor solutionfor inflation.
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