Constraints on field flows of quintessence dark energy

The quest for understanding the late-time acceleration is haunted by an immense freedom in the analysis of dynamical models for dark energy in extended parameter spaces. Often-times having no prior knowledge at our disposal, arbitrary choices are implemented to reduce the degeneracies between parameters. We also encounter this issue in the case of quintessence fields, where a scalar degree of freedom drives the late-time acceleration. In this study, we implement a more physical prescription, the \textit{flow} condition, to fine-tune the quintessence evolution for several field potentials. We find that this prescription agrees well with the most recent catalogue of data, namely supernovae type Ia, baryon acoustic oscillations, cosmic clocks and distance to last scattering surface, and it enables us to infer the initial conditions for the field, both potential and cosmological parameters. At $2\sigma$ we find stricter bounds on the potential parameters $f/m_{pl}>0.26$ and $n<0.15$ for the PNGB and IPL potentials, respectively, while constraints on cosmological parameters remain extremely consistent across all assumed potentials. By implementing information criteria to assess their ability to fit the data, we do not find any evidence against thawing models, which in fact are statistically equivalent to $\Lambda$CDM, and the freezing ones are moderately disfavoured. Through our analysis we place upper bounds on the slope of quintessence potentials, consequently revealing a strong tension with the recently proposed swampland criterion, finding the 2$\sigma$ upper bound of $\lambda \sim 0.31$ for the exponential potential.