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Inflection Point Quintessence

We examine models in which the accelerated expansion of the universe is driven by a scalar field rolling near an inflection point in the potential. For the simplest such models, in which the potential is of the form V(ϕ) = V_0 + V_3 (ϕ-ϕ_0)^3, the scalar field can either evolve toward ϕ= ϕ_0 at late times, yielding an asymptotic de Sitter expansion, or it can transition through the inflection point, producing a transient period of acceleration. We determine the parameter ranges which produce each of these two possibilities and also map out the region in parameter space for which the equation of state of the scalar field is close to -1 at all times up to the present, mimicking \LambdaCDM. We show that the latter can be consistent with either eternal or transient acceleration. More complicated inflection point models are also investigated.