Modified Symmetric teleparallel gravity in higher dimensions

In this work, a more general version of modified symmetric teleparallel gravity f(Q) gravity in six dimensions is conceptualized. Here the non-zero non-metricity tensor is the fundamental object, which is torsion-less and curvature-less. The most general field equations are found for a generic Lagrangian f(Q)+L, where f(Q) is a function of a quadratic scalar Q built from irreducible components of the nonmetricity tensor, and L is the matter Lagrangian. The interior and the exterior of the six-dimension axi-symmetric warped brane for a power-law model of f(Q) is studied. It is found that, in the absence of a bulk cosmological constant, the non-metricity of the spacetime yields to a warped compactified spacetime. Moreover, the non-metrcity induces a transition from six-dimensional AdS to dS spacetime in the exterior of the brane. The manuscript of this work is under preparation.