Modeling Dark Sector in Horndeski Gravity at First-Order Formalism

We investigate a cosmological scenario by finding solutions using first-order formalism in the Horndeski gravity that constrains the superpotential and implies that no free choice of scalar potential is allowed. Despite this, we show that a de Sitter phase at late-time cosmology can be realized, where the dark energy sector can be identified. The scalar field equation of state tends to the cosmological scenario at present time and allows us to conclude that it can simulate the dark energy in the Horndeski gravity.