Dark energy parametrizations in Einstein–Aether gravity with cubic curvature corrections

We investigate the late-time cosmic acceleration within the framework of generalized Einstein-Aether gravity incorporating cubic curvature corrections. Employing three widely used dynamical dark energy parametrizations-CPL, JBP, and BA, we reconstruct the cosmic expansion history by constraining the free model parameters using Type Ia Supernova (SN Ia) data from the Pantheon compilations via a ${\chi }^2$-minimization approach. We determine best-fit values for the model parameters and evaluate key cosmological quantities such as the dark energy density ${\Omega }_{{\text{de}}_0}$,the matter density ${\Omega }_{{\text{m}}_0}$, the Hubble constant $H_0$, and the deceleration parameter $q_0$ of the present universe. We also examine the evolution of the potential $V\left(z\right)$ and the kinetic energy $\frac{{\dot{\varphi }}^2}{2}$ of the equivalent scalar field representing dark energy as functions of redshift $z$.