Modified Emergent Dark Energy and its Astronomical Constraints

We introduce a modified form of the Phenomenologically Emergent Dark Energy (PEDE) model by showing a very elegant approach. The model is named as Modified Emergent Dark Energy (MEDE) to distinguish from PEDE model and it includes $\Lambda$CDM, PEDE model, Chevallier-Polarski-Linder model and other cosmological models of interest. We show that the present article offers a very fantastic route to construct other PEDE models in a simple but very elegant way. The model has seven free parameters where the six parameters are the same as in $\Lambda$CDM or PEDE model and the remaining one parameter `$\alpha$' quantifies the generalization. The present model predicts that dark energy equation of state at present assumes, $w_{\rm DE}\; (z=0) = -1 - \frac{\alpha}{3 \ln (10)}$ and in the far future (i.e., for $z \longrightarrow -1$), it will evolve asymptotically to $w_{\rm DE} \longrightarrow -1$. We perform a very robust observational analysis of the model using various observational datasets including cosmic microwave background radiation, baryon acoustic oscillations distance measurements, a local value of the Hubble constant and the pantheon sample of Supernovae Type Ia. We find that the $H_0$ tension here is alleviated but not solved, while the only free parameter, $\alpha$ could recover the $\Lambda$CDM or PEDE for different datasets. In summary, the present article describes a novel route to construct other modified versions of the PEDE model in a very simplified manner.