Quintessences Universe in $f(R, L_m)$ gravity with special form of deceleration parameter

Abstract: In this paper We have investigated a homogeneous and isotropic FRW cosmological model with perfect fluid in the framework of $f(R,Lm)$ gravity. We have explored for the non linear case of $f(R,L_m)$ model, namely $f(R,L_m) = R/2 + L_m$ and obtained the solution by using the condition that the deceleration parameter is a linear function of the Hubble parameter. We employ 57 Hubble data points and 1048 Pantheon supernovae type Ia data samples to restrict the model parameters. Additionally, we employ Markoc Chain Monte Carlo (MCMC) simulation for our statistical analysis. Additionally, we analyse the jerk and om diagnostic parameters for our model using the parameter values that were obtained.