This paper treats nonrelativistic matter and a scalar field $\varphi$ with a monotonically decreasing potential minimally coupled to gravity in flat Friedmann-Lemaître-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 global and asymptotic bounds on $\lambda =-V^{-1}dV/d\varphi$ to obtain viable cosmological models that continuously deform $\mathrm{\Lambda }\mathrm{CDM}$ cosmology. In particular we introduce a regularized inverse power-law potential as a simple specific example.

• Received 4 August 2015

DOI:https://doi.org/10.1103/PhysRevD.92.103502