Linear redshift parametrization of deceleration parameter in f (R, Lm) gravity

In this study, we investigate the linear redshift parametrization of q(z) within the framework of f(R, L-m) gravity, using constraints derived from H(z)/Pant heon samples. We consider a non-linear functional form for f(R, L-m), specifically given by f(R, L-m) = R/2 + L-m(n), where n represents a free parameter in the model. Subsequently, we derive the solution for the Hubble parameter by investigating the parametrization of q(z) and then apply this solution to the modified Friedmann equations. Our analysis focuses on exploring the behavior of the EoS parameter across different stages of the universe's evolution, including radiation, matter, and dark energy eras. Furthermore, our results confirm the quintessence nature of the universe's current accelerated expansion phase (-1 < omega < - 1/3), supporting the role of quintessence in driving the universe's current acceleration. We also explore the redshift dependence of the deceleration parameter, statefinder, Om(z) diagnostics, energy density, pressure, and energy conditions to determine the universe's accelerating behavior. Importantly, our findings suggest that the linear redshift parametrization of q(z), supported by additional terms in f(R, L-m) gravity, provides a compelling alternative to the cosmological constant.