Rahul Bhagat, I. V. Fomin, B. Mishra
ABSTRACT We investigate the logarithmic form of gravity with two different choices of matter Lagrangian such as: and . The parameters of the model have been constrained using Cosmic Chronometers (CC) in combination with DES‐SN5YR, Type Ia supernova and DESI DR2 (BAO) datasets. We have observed that the deceleration parameter shows a smooth transition from deceleration to acceleration phase and the effective equation of state parameter () approaches at late times. The diagnostic exhibits a decreasing profile, confirming quintessence‐like behavior, and the state finder analysis demonstrates trajectories that remain near the fixed point but deviate into the quintessence region. The evolution of the density parameters satisfies the flatness condition, and the predicted age of the Universe lies within Gyr, consistent with CMB and stellar estimates. The findings indicate that the logarithmic model successfully reproduces the late‐time accelerated expansion for both the choices of the matter Lagrangian.