Abstract
In this study, we have demonstrated the expansion history of an axially symmetric Bianchi type-I model of the universe. Our model as of now presents an accelerating universe, which had been in the decelerating phase in the past. Roles of the two crucial Hubble~$H(z)$ and deceleration~$q(z)$ parameters are examined. The energy parameters of the universe are estimated with the help of the latest observational Hubble data (46-data points) and Pantheon data (the latest compilation of SNIa with 40 binned in the redshift range $0.014 \leq z \leq 1.62)$. We also discuss the stability analysis of the model by state finder diagnosis. The analysis reveals that in late time, the model is a quintessence type and points towards the $\Lambda$CDM model. Our developed model agrees with observational findings in a proper way. We have discussed some of the physical aspects of the model.
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