Braneworlds in $f(Q)$ gravity

TL;DR

This paper explores a braneworld model within $f(Q)$ gravity, where nonmetricity influences brane structure, and introduces a geometric coupling that localizes chiral fermions, revealing new inner structures and particle spectra.

Contribution

It develops a novel braneworld scenario in $f(Q)$ gravity with scalar fields and nonmetricity, showing how modifications affect brane structure and fermion localization.

Findings

Brane acquires an inner structure and undergoes splitting.

A stable tower of massive fermion states is found.

Nonmetricity controls brane width and shape.

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 non-minimal 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 non-localized massive states.