Framework for Estimating Cosmological Parameters using Observational Cosmology and Artificial Neural Networks in f(R,T)$f(R, T)$ Gravity

An exact solution of bulk viscous Bianchi I universe is proposed in theory of gravity and its free parameters are probed using Bayesian MCMC and Artificial neural networks (ANNs) methods. In cosmology, analyzing observable evidence is critical for evaluating theoretical models of the universe. The ANNs are strong and adaptable computational tools for data modeling, and they have lately been used to analyze cosmic data. This study introduces ANNs and discusses their applications in cosmology. A general overview of neural networks is provided as well as technical specifics. Their capabilities in cosmological data modeling, numerical challenges, and star object categorization are demonstrated using three cases. ANNs provide intriguing properties that make them feasible options for data analysis in cosmological study. Parameters are estimated using a code called CoLFI, which combines the benefits of ANNs and can be used in any complex model parameter estimation across a variety of scientific domains. When the likelihood function is unmanageable or cosmological models are intricate and resource‐intensive, CoLFI offers a more effective method of parameter estimation. The model provides a mechanism to explain the late‐time acceleration of the universe by attributing it to modified gravitational dynamics and bulk viscous effects, rather than a distinct dark energy component. The transition Redshift from deceleration to acceleration phase is obtained as and from Bayesian and ANNs methods, respectively. Some physical and geometrical features of the model are also investigated.