For single-axion potentials of the form Λ0^3 b + Λ1^4 cos(b/fb), the paper classifies the fixed points of the Friedmann-Klein-Gordon dynamics into stable nodes/spirals, saddles, and a bifurcation at |γ/δ|=1.
Scalar field cosmology in phase space
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abstract
Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time quintessence eras. Focussing on the spatially flat case, we examine the geometrical structure of the phase space, locate the equilibrium points of the system (de Sitter spaces with a constant scalar field), study their stability through both a third-order perturbation analysis and Lyapunov functions, and discuss the late-time asymptotics. As we do not specify the scalar field's origin or its potential, the results are independent of the high-energy model.
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Dynamical-System analysis of single-axion monodromy inflation with periodically-modulated potentials
For single-axion potentials of the form Λ0^3 b + Λ1^4 cos(b/fb), the paper classifies the fixed points of the Friedmann-Klein-Gordon dynamics into stable nodes/spirals, saddles, and a bifurcation at |γ/δ|=1.