Constraining dark energy dynamics in extended parameter space

Dynamical dark energy has been recently suggested as a promising and physical way to solve the 3 sigma tension on the value of the Hubble constant H₀ between the direct measurement of Riess et al. (2016) (R16, hereafter) and the indirect constraint from cosmic microwave anisotropies obtained by the Planck satellite under the assumption of a model. In this paper, by parametrizing dark energy evolution using the w₀-w₀ approach, and considering a 12 parameter extended scenario, we find that: (a) the tension on the Hubble constant can indeed be solved with dynamical dark energy, (b) a cosmological constant is ruled out at more than 95% c. l. by the Planck+R16 dataset, and (c) all of the standard quintessence and half of the ``downward going'' dark energy model space (characterized by an equation of state that decreases with time) is also excluded at more than 95% c. l. These results are further confirmed when cosmic shear, CMB lensing, or SN Ia luminosity distance data are also included. The best fit value of the ^2 for the Planck+R16 data set improves by ^2=-12. 9 when moving to 12 parameters respect to standard. However, tension remains with the BAO dataset. A cosmological constant and small portion of the freezing quintessence models are still in agreement with the Planck+R16+BAO data set at between 68% and 95% c. l. Conversely, for Planck plus a phenomenological H₀ prior, both thawing and freezing quintessence models prefer a Hubble constant of less than 70 km/s/Mpc. The general conclusions hold also when considering models with nonzero spatial curvature.