A Bayesian Statistical Study of Bianchi Type-I Universe in f (R, Tψ) 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 estimate Hubble parameter, effective equation of state parameter ($\omega^{\text{eff}}$) and potential of scalar field as a function of time using equation $H=W(\psi)$. The graphical representation of 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 Markov Chain Monte Carlo (MCMC) mechanism on derived $H(z)$ model by using observational Hubble data (OHD), DESI Baryon Acoustic Oscillation (DESI BAO) dataset and Pantheon Type Ia Supernova 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.