Dynamic Dark Energy Equation of State (EoS) and Hubble Constant analysis using type Ia supernovae from Union 2.1 dataset

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.