Generalized emergent dark energy: observational Hubble data constraints and stability analysis

ABSTRACT Recently, a phenomenologically emergent dark energy (PEDE) model was presented with a dark energy density evolving as $\widetilde{\Omega }_{\rm {DE}}(z) = \Omega _{\rm {DE,0}}[ 1 - {\rm {tanh}}({\log }_{10}(1+z))]$, i.e. with no degree of freedom. Later on, a generalized model was proposed by adding one degree of freedom to the PEDE model, encoded in the parameter Δ. Motivated by these proposals, we constrain the parameter space ($h,\Omega _m^{(0)}$) and ($h,\Omega _m^{(0)}, \Delta$) for PEDE and generalized emergent dark energy (GEDE), respectively, by employing the most recent observational (non-)homogeneous and differential age Hubble data. Additionally, we reconstruct the deceleration and jerk parameters and estimate yield values at z = 0 of $q_0 = -0.784^{+0.028}_{-0.027}$ and $j_0 = 1.241^{+0.164}_{-0.149}$ for PEDE and $q_0 = -0.730^{+0.059}_{-0.067}$ and $j_0 = 1.293^{+0.194}_{-0.187}$ for GEDE using the homogeneous sample. We report values on the deceleration–acceleration transition redshift with those reported in the literature within 2σ CL. Furthermore, we perform a stability analysis of the PEDE and GEDE models to study the global evolution of the Universe around their critical points. Although the PEDE and GEDE dynamics are similar to the standard model, our stability analysis indicates that in both models there is an accelerated phase at early epochs of the Universe evolution.