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.
