Dynamical Dark Energy models in light of the latest observations

In this paper, we study several models and parameterizations of dynamical dark energy (DE) that have been studied already in the past, in conjunction with the recently proposed model $w$XCDM, the running vacuum model (RVM) with and without a threshold at $z=1$ and two variants of it, the RRVM and the ``flipped RVM'', and compare them all with the concordance $\Lambda$CDM model and the popular $w_0w_a$CDM parameterization. We use two standard sets of cosmological data, one including distant supernovae from Pantheon$+$ and the other from DES-Y5. The rest of the data (BAO from DESI DR2 and CMB from Planck PR4) are shared by the two sets. They are analyzed using the state-of-the-art techniques. No structure formation data are utilized for this analysis and no use is made of the SH0ES calibration of $H_0$. Even so, we find that the flipped RVM and to a lesser extent the $w$XCDM and the RVM with threshold, point to significant evidence of dynamical DE, at a level comparable to $w_0w_a$CDM, more conspicuously for the dataset that involves DES-Y5 observations. We also find that while more traditional models studied in the past, in which there is an exchange between vacuum energy and cold dark matter (through e.g. an interactive source proportional either to the density of dark matter or to that of vacuum) still hint at dynamical DE, the strength of the statistical signal (which we assess through information criteria and other estimators) is nevertheless less pronounced. Finally, we discuss the ability of the various models to explain the data by performing an analysis of their effective equation-of-state parameters and corresponding evolution of their dark energy densities.