Thick brane in mimetic f(T) gravity

We apply the mimetic f(T) theory into the thick brane model. We take the Lagrange multiplier formulation of the action and get the corresponding field equations of motion. We find solutions for different kinds of f(T). Besides, we investigate the stability of the mimetic f(T) brane by considering the tensor perturbations of the vielbein. Localization problem is also studied and it is shown that the four-dimensional gravity can be recovered for all the solutions. The effects of the torsion show that for the polynomial form of f(T), the zero mode has a split compared with that of f(T) = T, but the situations for the exponential form of f(T) are similar to that of f(T) = T. (C) 2019 The Authors. Published by Elsevier B.V.