Bouncing universe scenarios in an extended gravitational framework involving curvature-matter coupling

Exploration of bouncing cosmic models in modified theories has gained much popularity in modern cosmology. This paper explores the Lagrangian function of a new theory namely $F(R,L_m,T)$ framework by taking four renowned cosmic bouncing models, i.e., the exponential bounce, oscillatory bounce scenario, power law, and matter bouncing. Our primary objective is to fix the form of $F(R,L_m,T)$ function for each model and investigate which kinds of reconstructed Lagrangian function have potential of regenerating bouncing scenario in terms of analytical form. It is seen that except power law model, the analytical solutions are conceivable only for certain cases of these bouncing models. For power law bounce, different cases of Lagrangian function may be rebuilt analytically while for some other bouncing scenarios, it is found that particular solutions are not always attainable and hence only the complimentary solutions can be explored. Further, we examine the behavior of energy constraints and stability of these analytically formed bouncing solutions. Additionally, we determine that the dark energy phase in $F(R,L_m,T)$ gravity is compatible with the experimental data of BAO+Sne-Ia+CMB+H(z) and it is shown that cosmic bounce can be produced with dark energy eras in this gravity. We also present some constraints on the model parameters with Hubble parameter values and ΛCDM to determine the best-fit values of model via least square and reduced chi-squares methods. It is concluded that matter bounce model is the best fitted with the observational data set as well as ΛCDM model because it has least value of ${\chi }_m^2$.