Thick brane in mimetic $f(T)$ gravity

Abstract

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 $f(T)=T$.

7 pages, 6 figures

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• Fundamental energy scale of the thick brane in mimetic gravity
• Thick string-like braneworlds in f(T) gravity
• Geometrically contracted structure in teleparallel $f(T)$ gravity
• Teleparallel gravity: Effects of torsion in 6D braneworlds
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Effects of Cuscuton dynamics on braneworld configurations in the scalar-tensor representation of $f\left(R,T\right)$ gravity
• Thick branes in the scalar-tensor representation of $f(R,T)$ gravity