Dark energy nature of logarithmic f(R, Lm)-gravity models with observational constraints

This work explores the dark energy nature of logarithmic F(R, L-m)-gravity models with observational constraints, where L-m represents the matter Lagrangian for perfect fluid and R is the Ricci-scalar curvature. With a matter Lagrangian L-m = rho, a flat FLRW space-time metric and an arbitrary function F(R, L-m) = R/2 + L-m - ln L-m, where mu is a positive model parameter, we have derived the field equations of this model. By using the Hubble function, we have been able to solve the energy conservation equation and create a relationship between Omega(m0), Omega(q0) and Omega(mu 0). Using the most recent two observational datasets as 32 H(z) and 1048 Pantheon SNe Ia datasets, we conducted MCMC analysis. We have obtained best fit values of model parameters with 1 - sigma, 2 - sigma, 3 - sigma errors and using these values, we have explored the cosmological properties of the model. We have performed om diagnostic analysis for the model and estimated the present age of the universe. Thus our derived model presents a transit phase decelerating to accelerating model without dark energy term Lambda. We found that the effective equation of state parameter is in the range -1 <= omega <= 0 over -1 <= z < infinity with present value omega approximate to -0.6971,-0.7120.