A Bayesian Statistical Study of Bianchi Type-I Universe in $f(R,T^\psi)$ Modified Gravity

We have examined the cosmological actions of LRS (Locally Rationally Symmetric) Bianchi type-I universe model in $f(R,T^\psi)$ gravity. For this, we have estimated the Hubble parameter, the effective equation of state parameter ($\omega^{eff}$), and the potential of the scalar field as a function of time using equation $H = W(\psi)$. The graphical representation of the potential function $V(\psi)$ with respect to cosmic time t is described. This study explores the dynamical properties of a Bianchi Type-I universe by utilizing Bayesian statistical techniques to constrain the model parameters and evaluate the viability of anisotropic cosmology under extended matter-geometry couplings. Also, we have applied the Markov Chain Monte Carlo (MCMC) mechanism on the derived $H(z)$ model by using observational Hubble data (OHD), the Baryon Acoustic Oscillation (BAO) dataset, and the Pantheon dataset. From the confidence-level contours and best-fit parameter values obtained, along with the corresponding reduced $\chi^{2}$, it is evident that the model aligns strongly with observational data, demonstrating statistical stability and consistency in describing late-time cosmic acceleration. Likewise, the error analyses presented in this research, including a comparison between the $\Lambda$CDM cosmology and the reconstructed $H(z)$ model, confirm the model's compatibility with current observations by yielding a reliable and accurate account of the universe's expansion history.