Constraining f(R,Lm) gravity with SN Ia and BAO observational data in Bianchi I space time

In this study, we investigate the viability of the $f(R,L_m)$ gravity framework in explaining the accelerated expansion of the universe within the context of the locally rotationally symmetric (LRS) Bianchi-I space-time. Modified gravity theories have emerged as promising alternatives to General Relativity (GR) to account for cosmic acceleration and dark energy phenomena. We employ observational constraints from Type Ia Supernovae (SN Ia), Baryon Acoustic Oscillations (BAO), and Cosmic Chronometers (CC) to calibrate the free parameters of our model. The field equations are formulated based on a specific functional form of $f(R,L_m)$, and analytical solutions are obtained. The Hubble parameter, deceleration parameter ($q$), statefinder diagnostics $(r,s)$, and the jerk parameter ($j$) are utilized to analyze the evolutionary dynamics of the universe. Our results indicate a transition from a decelerating to an accelerating phase, with the transition redshift $z_t=0.{7293}_{-0.06}^{+0.07}$ and present deceleration parameter $q_0=-0.56$, consistent with observational data. The estimated age of the universe in this framework is $13.27\pm 0.26$ Gyrs. The statefinder parameters suggest that the model closely mimics the standard $\Lambda$CDM scenario at present but exhibits deviations at earlier epochs, potentially indicating a dynamic nature of dark energy. The $O_m$ diagnostic further confirms the compatibility of our model with a phantom-like behavior of dark energy. These findings support the viability of $f(R,L_m)$ gravity as an alternative framework for explaining cosmic acceleration, providing new interplay between matter and curvature in gravitational dynamics.