Inspired by the string axiverse idea, it has been suggested that the recent transition from decelerated to accelerated cosmic expansion is driven by an axion-like quintessence field with a sub-Planckian decay constant. The scenario requires that the axion field be rather near the maximum of its potential, but is less finely tuned than other explanations of cosmic acceleration. The model is parametrized by an axion decay constant $f$, the axion mass $m$, and an initial misalignment angle $|theta_i|$ which is close to $pi$. In order to determine the $m$ and $theta_{i}$ values consistent with observations, these parameters are mapped onto observables: the Hubble parameter $H(z)$ at and angular diameter distance $d_{A}(z)$ to redshift $z= 0.57$, as well as the angular sound horizon of the cosmic microwave background (CMB). Measurements of the baryon acoustic oscillation (BAO) scale at $zsimeq 0.57$ by the BOSS survey and Planck measurements of CMB temperature anisotropies are then used to probe the $left{m,f,theta_iright}$ parameter space. With current data, CMB constraints are the most powerful, allowing a fraction of only $sim 0.2$ of the parameter-space volume. Measurements of the BAO scale made using the SPHEREx or SKA experiments could go further, observationally distinguishing all but $sim 10^{-2}$ or $sim 10^{-5}$ of the parameter-space volume (allowed by simple priors) from the $Lambda$CDM model.
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