Cosmological implications of dark energy with bouncing scenario in f(R,Lm) gravity

This work examines the bouncing model integrated with Dark Energy (DE) in a flat Friedmann–Robertson–Walker (FRW) Universe within [Formula: see text] gravity. We consider the minimal coupling model as [Formula: see text], with a focus on the cosmic speed singularity over time with bouncing conduction analysis. We highlight the implications of the model’s dynamic parameters along with those of the bouncing scale factor. The Equation of State (EoS) parameter [Formula: see text] sets forth the approach to DE under exploration that dictates the Universe’s bouncing conduct by transitioning across the quintom line [Formula: see text]. We explored numerous Energy Conditions (ECs) in this scenario. The diagnostic pair of statefinder [Formula: see text], together with the jerk parameter [Formula: see text] are examined in order to reveal substantial variations in cosmic eras. We worked with the squared sound speed parameter [Formula: see text] to suit the requirements of our model’s stability. Our studies transpired that the results obtained lined up with recent observational evidence, providing a way via [Formula: see text] gravity framework for addressing both cosmic acceleration while participating in the issue of singularity encountered in the Cosmos.