First-Order Formalism and Thick Branes in Mimetic Gravity

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired considering the conformal symmetry under transformation of an auxiliary metric. By introducing two super-potentials, transform second-order equations system into set first-order equations. With formalism, several types analytical brane solutions are obtained. Then, tensor and perturbations analyzed. We find that both kinds stable. The effective potentials for dual to each other. zero mode can be localized on while cannot. Thus, four-dimensional Newtonian potential recovered brane.