Has DESI detected exponential quintessence?

The new Dark Energy Spectroscopic Instrument (DESI) DR2 results have strengthened the possibility that dark energy is dynamical, i.e., it has evolved over the history of the Universe. One simple, but theoretically well motivated and widely studied, physical model of dynamical dark energy is minimally coupled, single-field quintessence $\phi$ with an exponential potential $V(\phi)=V_0\,e^{-\lambda\phi}$. We perform a full Bayesian statistical analysis of the model using the DESI DR2 data, in combination with other cosmological observations, to constrain the model's parameters and to compare its goodness of fit to that of the standard $\Lambda$CDM model. We find that the quintessence model provides a significantly better fit to the data, both when the spatial curvature of the Universe is fixed to zero and when it is allowed to vary. The significance of the preference varies between $\sim3.3\sigma$ and $\sim3.8\sigma$, depending on whether the curvature density parameter $\Omega_K$ is fixed or varied. We obtain the values $0.698^{+0.173}_{-0.202}$ and $0.722^{+0.182}_{-0.208}$ at the $68.3\%$ (i.e., $1\sigma$) confidence level for the parameter $\lambda$ in the absence and presence of $\Omega_K$, respectively, which imply $\sim3.5\sigma$ preference for a nonzero $\lambda$. We also obtain $\Omega_K=0.003\pm 0.001$, which implies $\sim3\sigma$ preference for a positive $\Omega_K$, i.e., a negative curvature. Finally, we discuss the differences between quintessence and phenomenological parametrizations of the dark energy equation-of-state parameter, in particular the Chevallier-Polarski-Linder (CPL) parametrization, as well as a few caveats to our results.