Phenomenological Dark Energy model with hybrid dynamic Cosmological
  Constant
  We investigate Dark Energy by associating it with vacuum energy or
Cosmological constant ${\Lambda}$ which is taken to be dynamic in nature. Our
approach is phenomenological and falls within the domain of variable-$\Lambda$
Cosmology. However, motivated by quantum theory of metastable vacuum decay, we
proposed a new phenomenological decay law of $\Lambda$(t) where $\Lambda$(t) is
a superposition of constant and variable components viz. $\Lambda$(t) =
$\Lambda_{C}$ + $\Lambda_{v}$ which is indicated by the word $"$hybrid
dynamic$"$ in the title. By taking a simplified two-fluid scenario with the
Universe consisting of Dark Energy and another major component, we found the
solutions for three particular phenomenological expressions and made a
parametrization of the model in terms of dilution parameter (the dilution
parameter has been defined in the text as the exponent of scale factor in the
expression of density of the other major component, representing the dilution
of the component with the expansion of Universe in the presence of dynamic Dark
Energy). For pressureless Dust and dynamic Dark Energy Universe, we found the
present-day matter density ($\Omega_{m0}$) and dilution parameter (u) to be
$\Omega_{m0}$ = 0.29 $\pm$ 0.03, u = 2.90 $\pm$ 0.54 at 1 $\sigma$ by analysing
580 supernova from Union 2.1 catalogue. The physical features of the model in
regard to scale factor evolution, deceleration parameter, cosmic age has also
been studied and parallels have been drawn with $\Lambda$CDM model. The status
of Cosmological problems in the model has also been checked which showed that
the model solves the Cosmological Constant Problem but the Coincidence problem
still exists in the model.
