Statistical Constraints on Anisotropic Bianchi-III Cosmology in $f(R,T)$-Gravity Using MCMC Methods

Anisotropic Bianchi type-III cosmology is examined within the framework of f(R,T) gravity, where R denotes the Ricci scalar and T the trace of the energy-momentum tensor. In this work, we investigate the statistical constraints on anisotropic Bianchi type-III cosmology within the framework of f(R,T) gravity. The specific choice $f(R,T)=R+2f(T)$ is considered and exact solutions are derived for the background dynamics of the model. The physical parameters, such as the Hubble parameter H(z), spatial volume V(z), energy density $\rho(z)$, and pressure p(z), are derived and their evolutionary behaviors are analyzed. To examine the observational viability of the model, we employ Markov Chain Monte Carlo (MCMC) methods and perform a comprehensive statistical analysis using the latest observational datasets, including the Hubble parameter measurements, Baryon Acoustic Oscillations (BAO), and the Pantheon compilation of type Ia supernovae. The combined data analysis provides constraints on the free parameters of the model and allows a comparison with the standard $\Lambda$CDM cosmology. Our results show that the anisotropic Bianchi-III universe in f(R,T) gravity can successfully accommodate current observational data, offering new insights into the role of matter-geometry coupling in the late-time cosmic acceleration.