Observational constraints on inflection point quintessence with a cubic potential

We examine the simplest inflection point quintessence model, with a potential given by $V(ϕ) = V_0 + V_3 ϕ^3$. This model can produce either asymptotic de Sitter expansion or transient acceleration, and we show that it does not correspond to either pure freezing or thawing behavior. We derive observational constraints on the initial value of the scalar field, $ϕ_i$, and $V_3/V_0$ and find that small values of either $ϕ_i$ or $V_3/V_0$ are favored. While most of the observationally-allowed parameter space yields asymptotic de Sitter evolution, there is a small region, corresponding to large $V_3/V_0$ and small $ϕ_i$, for which the current accelerated expansion is transient. The latter behavior is potentially consistent with a cyclic universe.

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