Abstract
This paper treats nonrelativistic matter and a scalar field $\phi$ with a monotonically decreasing potential minimally coupled to gravity in flat Friedmann-Lema\^{i}tre-Robertson-Walker cosmology. The field equations are reformulated as a three-dimensional dynamical system on an extended compact state space, complemented with cosmographic diagrams. A dynamical systems analysis provides global dynamical results describing possible asymptotic behavior. It is shown that one should impose \emph{global and asymptotic} bounds on $\lambda=-V^{-1}\,dV/d\phi$ to obtain viable cosmological models that continuously deform $\Lambda$CDM cosmology. In particular we introduce a regularized inverse power-law potential as a simple specific example.
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