Observational constraints in late time for an axially symmetric transitioning model with bulk viscous fluid

Abstract: In this paper, we explore an axially symmetric Bianchi type-I model of the universe with bulk viscous fluid as a source of gravitational field under the framework of Einstein's field equations by assuming barotropic bulk viscous pressure as $-3\zeta H^2$. The model parameters have been estimated with the help of four data sets: The Hubble 46 data set describes Hubble parameter values at various redshifts, Union 2.1 compilation data sets comprise a distance modulus of 580 SNIa supernovae at different redshifts, the Pantheon data set contains Apparent magnitudes of 1048 SNIa supernovae at various redshifts and finally BAO data set of volume averaged distances at 5 redshifts. The observational data is analyzed using the traditional Bayesian methodology, and the posterior distributions of the parameters are obtained using the Markov Chain Monte Carlo (MCMC) technique. To get the best-fit values for the model parameters for MCMC analysis, we use the $ emcee $ package. For parameter estimation, we have also employed the minimizing $\chi^{2}$ function. We also tried to achieve these values statistically using combined data sets from the four described earlier. The OHD+BAO~and~OHD+Pan+BAO+Union combined data sets provide the best fit Hubble parameter value $H_0$ as $66.912 ^{+0.497}_{-0.501})$ Km/s/Mpc and $74.216 ^{+0.150}_{-0.148}$ Km/s/Mpc respectively. We have performed state finder diagnostics to discuss the nature of dark energy. Some other geometrical parameters like the Jerk parameter and the Om diagnostic are also being discussed to clarify the nature of the dark energy model. The study reveals that the model behaves like a quintessence in late time and approaches the $\Lambda$ CDM model.