Late-time dynamics of the John–George model with exponential potential in non-minimal derivative coupling cosmology

In this work, we numerically investigate the cosmological evolution of a non-minimal derivative coupling model with a scalar potential term coupled to the Ricci scalar. Specifically, we focus on the late-time cosmology of the John–George field model. By adopting the FLRW metric, we derive the equations of motion corresponding to the scalar field configuration. We then construct a system of equations, which is solved numerically using two well-known types of potentials from the literature: the power-law potential and the exponential potential. To characterize the dynamics, we evaluate key cosmological quantities such as the Hubble parameter, the statefinder diagnostic, and dark energy indicators including the equation of state and energy density. The numerical evolution of these parameters reveals a phenomenology consistent with the latest Planck 2018 observations. Moreover, the model successfully reproduces the behavior of the standard [Formula: see text]-Cold Dark Matter ([Formula: see text]CDM) cosmological model, supporting its viability as an alternative framework for describing late-time cosmic acceleration.