Dynamical dark energy: scalar fields and running vacuum

Recent analyses in the literature suggest that the concordance $\Lambda$CDM model with rigid cosmological term, $\Lambda=$const., may not be the best description of the cosmic acceleration. The class of "running vacuum models", in which $\Lambda=\Lambda(H)$ evolves with the Hubble rate, has been shown to fit the string of $SNIa+BAO+H(z)+LSS+CMB$ data significantly better than the $\Lambda$CDM. Here we provide further evidence on the time-evolving nature of the dark energy (DE) by fitting the same cosmological data in terms of scalar fields. As a representative model we use the original Peebles & Ratra potential, $V\propto\Phi^{-\alpha}$. We find clear signs of dynamical DE at $\sim 4\sigma$ c.l., thus reconfirming through a nontrivial scalar field approach the strong hints formerly found with other models and parametrizations.