  We investigate constraints on some key cosmological parameters by confronting
metastable dark energy models with different combinations of the most recent
cosmological observations. Along with the standard $\Lambda$CDM model, two
phenomenological metastable dark energy models are considered: (\romannumeral1)
DE decays exponentially, (\romannumeral2) DE decays into dark matter. We find
that: (1) when considering the most recent supernovae and BAO data, and
assuming a fiducial $\Lambda$CDM model, the inconsistency in the estimated
value of the $\Omega_{\rm{m,0}}h^2$ parameter obtained by either including or
excluding Planck CMB data becomes very much substantial and points to a clear
tension~\citep{sahni2014model,zhao2017dynamical}; (2) although the two
metastable dark energy models that we study provide greater flexibility in
fitting the data, and they indeed fit the SNe Ia+BAO data substantially better
than $\Lambda$CDM, they are not able to alleviate this tension significantly
when CMB data are included; (3) while local measurements of the Hubble constant
are significantly higher relative to the estimated value of $H_0$ in our models
(obtained by fitting to SNe Ia and BAO data), the situation seems to be rather
complicated with hints of inconsistency among different observational data sets
(CMB, SNe Ia+BAO and local $H_0$ measurements). Our results indicate that we
might not be able to remove the current tensions among different cosmological
observations by considering simple modifications of the standard model or by
introducing minimal dark energy models. A complicated form of expansion
history, different systematics in different data and/or a non-conventional
model of the early Universe might be responsible for these tensions.
