In this study, we perform a comprehensive data analysis of \((2+1)\) -dimensional \(\Lambda (R,T)\) gravity with observational data sets from baryon acoustic oscillations (BAO), the Pantheon (SN) and Hubble data using Markov Chain Monte Carlo (MCMC) methods. Here the model parameters are constrained through statistical fitting to assess the viability of anisotropic cosmology within this modified gravity framework. Our results show that f(R, T) gravity with \(\Lambda (z)\) remains consistent with the late-time accelerated expansion of the universe, whereas the combined datasets yield tighter bounds on the free parameters. This highlights the significant role of matter-geometry coupling in shaping cosmic evolution. In general, \((2+1)\) -D \(\Lambda (z)\) gravity emerges as a promising alternative to the standard \(\Lambda\) -CDM scenario in explaining observational cosmology. This study introduces a redshift-dependent cosmological term \(\Lambda (z)\) within the \((2+1)\) -dimensional modified gravity framework, extending the conventional \(\Lambda\) CDM scenario. The model predicts a natural transition of \(\Lambda (z)\) from a decaying phase at high redshift to a nearly constant value at late times, consistent with the universe’s accelerated expansion. Through MCMC analysis using BAO, Pantheon, and Hubble datasets, the model parameters \((n, k_1, k_2, \lambda )\) are constrained, offering a new perspective on the cosmological constant problem in lower-dimensional gravity.
