Scalar field dark energy: Insights into cosmological evolution and black hole accretion

We propose a novel approach to parameterize the equation of state for Scalar Field Dark Energy (SFDE) and use it to derive analytical solutions for various cosmological parameters. Using statistical MCMC with Bayesian techniques, we obtain constraint values for the model parameters and analyze three observational datasets. We find a quintessence-like behavior for Dark Energy (DE) with positive values for both model parameters $\alpha$ and $\beta$. Our analysis of the $CC$+$BAO$+$SNe$ datasets reveals that the transition redshift and the current value of the deceleration parameter are $z_{tr}=0.73_{-0.01}^{+0.03}$ and $q_{0}=-0.44_{-0.02}^{+0.03}$, respectively. We also investigate the fluid flow of accretion SFDE around a Black Hole (BH) and analyze the nature of the BH's dynamical mass during accretion, taking into account Hawking radiation and BH evaporation. Our proposed model offers insight into the nature of DE in the Universe and the behavior of BHs during accretion.