Braneworlds in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-struck">Q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> gravity
J. E. G. Silva, R. V. Maluf, Gonzalo J. Olmo, C. A. S. Almeida
Abstract
We propose a braneworld scenario in a modified symmetric teleparallel gravitational theory, where the dynamics for the gravitational field is encoded in the nonmetricity tensor rather than in the curvature. Assuming a single real scalar field with a sine-Gordon self-interaction, the generalized quadratic nonmetricity invariant $\mathbb{Q}$ controls the brane width while keeping the shape of the energy density. By considering power corrections of the invariant $\mathbb{Q}$ in the gravitational Lagrangian, the sine-Gordon potential is modified exhibiting new barriers and false vacuum. As a result, the domain wall brane obtains an inner structure, and it undergoes a splitting process. In addition, we also propose a nonminimal coupling between a bulk fermion field and the nonmetricity invariant $\mathbb{Q}$. Such geometric coupling leads to a massless chiral fermion bound to the 3-brane and a stable tower of nonlocalized massive states.