Constraining the emergent dark energy models with observational data at intermediate redshift

In this work, we investigate the phenomenologically emergent dark energy (PEDE) model and its generalized form, namely the generalized emergent dark energy (GEDE) model, which introduces a free parameter \(\Delta \) that can discriminate between the \(\Lambda \)CDM model and the PEDE model. Fitting the emergent dark energy (EDE) models with the observational datasets including the cosmology-independent gamma-ray bursts (GRBs) and the observational Hubble data (OHD) at intermediate redshift, we find a large value of \(H_{0}\) which is close to the results of local measurement of \(H_{0}\) from the SH0ES Collaboration in both EDE models. In order to refine our analysis and tighten the constraints on cosmological parameters, we combine mid-redshift observations GRBs and OHD with baryon acoustic oscillations (BAOs). Finally, we constrain DE models by using the simultaneous fitting method, in which the parameters of DE models and the relation parameters of GRBs are fitted simultaneously. Our results suggest that PEDE and GEDE models can be possible alternative to the standard cosmological model, pending further theoretical explorations and observational verifications.