Dust-fluid accelerating flat cosmological models in f(R,T,Lm)-gravity with observational constraints

In this paper, we investigate dust-fluid flat cosmological models in the recently proposed modified [Formula: see text]-gravity theory. We derive the field equations for the flat FLRW spacetime metric for the arbitrary function [Formula: see text], where [Formula: see text] is the Ricci curvature scalar, [Formula: see text] is the matter Lagrangian, [Formula: see text] is the trace of the energy–momentum tensor [Formula: see text], and [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are the model parameters. We solve these equations to obtain the Hubble function in terms of matter energy density parameters [Formula: see text], [Formula: see text], [Formula: see text], and Hubble constant [Formula: see text]. Then, we use the cosmic chronometer (CC) Hubble points dataset and the Pantheon dataset to do MCMC analysis of the Hubble function and find the best fit model parameters for the lowest [Formula: see text] values. Subsequently, we investigate the effective equation of state parameter [Formula: see text] and deceleration parameter [Formula: see text] for the present past epoch of the universe. We also perform analysis for energy conditions and statefinder parameters to discuss the different stages of the dark energy models.