Thick branes in Born-Infeld determinantal gravity in Weitzenb\"ock spacetime

By adopting the idea of Born-Infeld electromagnetism, the Born-Infeld determinantal gravity in Weitzenb\"ock spacetime provides a way to smooth the Big Bang singularity at the classical level. We consider a thick braneworld scenario in the higher-dimensional extension of this gravity, and investigate the torsion effects on the brane structure and gravitational perturbation. For three particular parameter choices, analytic domain wall solutions are obtained. They have a similar brane configuration that the brane thickness becomes thinner as the spacetime torsion gets stronger. For each model, the massless graviton is localized on the brane with the width of localization decreasing with the enhancement of the spacetime torsion, while the massive gravitons propagate in the bulk and contribute a correction term proportional to ${1}/{(k r)^{3}}$ to the Newtonian potential. A sparsity constraint on the fundamental 5-dimensional gravitational scale is estimated from the gravitational experiment. Moreover, the parameter ranges in which the Kaluza-Klein gravitons are tachyonic free are analyzed.