Observational constraints on the expansion scalar and shear relation in the Locally rotationally symmetric Bianchi I model

We consider the universe composed of radiation, matter, and vacuum energy in the axially symmetric Bianchi I spacetime background. In this framework, the assumption 'shear scalar proportional to the expansion scalar' leading to a relation between directional scale factors has been probed for its observational compatibility with the data of different origins. The phase space of the model parameters is determined through the Bayesian Monte Carlo method. The precise observational bounds on parameters including n have been obtained with the cosmic chronometer, baryonic acoustic oscillations, cosmic microwave background, and the Supernovae Ia Pantheon data. The results are then compared with the results obtained by using the Pantheon+SH0ES data and the combined data sets. The deviations of n from unity change the cosmic dynamics during the early and late time universe also, as compared to the A cold dark matter model. We also discuss the information criterion in the model.