Thermodynamical aspects of Bianchi type-I Universe in quadratic form of $f\left( Q\right) $ gravity and observational constraints

In this paper, we discuss the Bianchi type-I cosmological model in the framework of symmetric teleparallel gravity say $f(Q)$ gravity in which the non-metricity term $Q$ is responsible for the gravitational interaction. We consider a special form of the $f\left( Q\right) $ function which can be cast as $f\left( Q\right) =\lambda Q^{n}$, where $\lambda $ and $n$ both are the dynamical model parameters. Such a choice can be viewed as a hybrid scale factor that leads to a relation between cosmic time and redshift as $% t=\left( \frac{\alpha t_{0}}{\beta }\right) W\left[ \frac{\beta }{\alpha }e^{% \frac{\beta -\ln \left( 1+z\right) }{\alpha }}\right] $ which describes a $% \Lambda $CDM model of the Universe with the expansion evolving from decelerating to an acceleration phase. The best values for the model parameters i.e. $\alpha $ and $\beta $ that would accord with the most current observational datasets are then estimated. We make use of 57 points from the Hubble dataset, 1048 points from the supernovae of type Ia dataset and 6 points from the BAO dataset. We use the Markov Chain Monte Carlo (MCMC) technique in conjunction with Bayesian analysis and the likelihood function. Further, we study the validity of our model with the investigation of the thermodynamical quantities, energy conditions along with some physical variables such as the EoS, and jerk parameters. Next, our results are discussed in light of current observational data and trends.