Constraining anisotropic f(R) cosmologies through observational data analysis

The present study explores the cosmological dynamics of an LRS Bianchi Type-I universe in the context of f ( R ) gravity, focusing on vacuum solutions. Two anisotropic models are constructed by considering different functional forms of f ( R ), where plane-symmetric LRSBI metrics incorporate anisotropy in the expansion rates, maintaining directional differences among Hubble parameters and scale factors throughout cosmic evolution. While such anisotropic assumptions in general relativity typically lead to a decelerating universe, functional forms of f ( R ) can support both accelerating and decelerating expansion branches, depending on the corresponding model parameters. To constrain the model parameters, we perform a comprehensive statistical analysis using Markov chain Monte Carlo (MCMC) methods with Hubble, BAO, and Pantheon datasets. The resulting observational constraints are interpreted at the level of the effective mean-background expansion. Model I and II constraints are illustrated through posterior contour and error bar plot, and the corresponding statistical values are summarized in tables.