Generalized Emergent Dark Energy Model and the Hubble Constant Tension

We investigate a generalized form of the phenomenologically emergent dark energy model, known as generalized emergent dark energy (GEDE), introduced by Li and Shafieloo [Astrophys. J. {\bf 902}, 58 (2020)] 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 phenomenologically emergent dark energy (PEDE) (corresponds to $\Delta=1$) models, allowing us to determine which model is preferred most by the fit of the observational datasets. We find evidence in favor of the GEDE model for Planck alone and in combination with R19, while the Bayesian model comparison is inconclusive when Supernovae Type Ia or BAO data are included. 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 $1\sigma$ CL.