Anisotropic behavior of universe in $$f(R, L_m)$$ f ( R , L m ) gravity with varying deceleration parameter

Abstract In this research study, we investigate the anisotropic behavior of the Universe using the framework of $$f(R, L_m)$$ f ( R , L m ) gravity. This modified gravity theory, represented by $$f(R, L_m)=\frac{R}{2}+L^\alpha _m+\beta $$ f ( R , L m ) = R 2 + L m α + β , incorporates both the Ricci scalar (R) and matter Lagrangian density ( $$L_m$$ L m ). Our exploration centers around understanding the Universe’s dynamics through the variable deceleration parameter. Additionally, we employ energy conditions, the jerk parameter, equation-of-state (EoS) parameter and statefinder parameters as analytical tools to gain insights into the evolution of the Universe within this modified gravity scenario. Our findings are then compared to recent observational data and are found to be in agreement with the $$\Lambda $$ Λ CDM model. This research contributes valuable insights into the anisotropic nature of the Universe in the context of $$f(R, L_m)$$ f ( R , L m ) gravity and highlights its deviations from the $$\Lambda $$ Λ CDM model, providing a deeper understanding of the fundamental dynamics of our cosmic evolution.