  This paper constraints dynamic dark energy equation of state (EoS) parameters
using the type Ia supernovae from Union 2.1 dataset. The paper also discusses
the dependency of dynamic dark energy EoS parameters on the chosen or assumed
value of the Hubble Constant. To understand the correlation between the Hubble
Constant values and measured dynamic dark energy EoS parameters, we used recent
surveys being done through various techniques such as cosmic microwave
background studies, gravitational waves, baryonic acoustic oscillations and
standard candles to set values for different Hubble Constant values as fixed
parameters with CPL and WCDM models. Then we applied trust region reflective
(TRF) and dog leg (dogbox) algorithms to fit dark energy density parameter and
dynamic dark energy EoS parameters. We found a significant negative correlation
between the fixed Hubble Constant parameter and measured EoS parameter, w0.
Then we used two best fit Hubble Constant values (70 and 69.18474) km $s^{-1}$
$Mpc^{-1}$ based on Chi-square test to test more dark energy EoS parameters
like: JBP, BA, PADE-I, PADE-II, and LH4 models and compared the results with
$\Lambda$-CDM with constant $w_{de}$=-1, WCDM and CPL models. We conclude that
flat $\Lambda$-CDM and WCDM models clearly provide best results while using the
BIC criteria as it severely penalizes the use of extra parameters. However, the
dependency of EoS parameters on Hubble Constant value and the increasing
tension in the measurement of Hubble Constant values using different techniques
warrants further investigation into looking for optimal dynamic dark energy EoS
models to optimally model the relation between the expansion rate and evolution
of dark energy in our universe.
