Generalized Emergent Dark Energy Model and the Hubble Constant Tension

We investigate a generalized form of the Phenomenologically Emergent Dark Energy (PEDE) model, known as Generalized Emergent Dark Energy (GEDE), introduced in~\cite{Li:2020ybr} in light of a series of cosmological probes and considering the evolution of the model at the level of linear perturbations. This model introduces a free parameter $\Delta$ that can discriminate between the $\Lambda$CDM (corresponds to $\Delta=0$) or the PEDE (corresponds to $\Delta=1$) models, allowing us to determine which model is preferred most by the fit of the observational datasets. We find a strong evidence of the GEDE scenario for most of the employed observational datasets. In particular, we find that $\Lambda$CDM model is disfavored at more than $2\sigma$ CL for most of the observational datasets considered in this work and PEDE is in agreement with Planck 2018+BAO+R19 combination within $1\sigma$. Finally, a Bayesian Model comparison shows a strong evidence for GEDE against $\Lambda$CDM for most of the dataset combinations.