Quasinormal modes of the thick braneworld in $f(T)$ gravity

We investigate the quasinormal modes (QNMs) of a thick brane model in $f(T)$ gravity with $f(T) = T + \alpha T^2$. Requiring the energy density to remain positive and the scalar field to be real constrains the parameter $\alpha$ to the range $[-\frac{7}{48},\frac{1}{48}]$. Within this allowed region, we find that the parameter $\alpha$ can induce a brane-splitting structure. The quasinormal frequencies of the system are computed using both the asymptotic iteration method and the Bernstein spectral method. The two approaches show good agreement in the low-overtone regime. For $\alpha<0$, the decay rate of the first QNM decreases as $|\alpha|$ increases, whereas higher overtones exhibit the opposite behavior. To further examine the influence of model parameters on the QNM spectrum, we also perform numerical time-domain evolution of perturbations, whose results are consistent with the frequency-domain analysis. Our results provide a concrete example of quasinormal spectra in thick brane models within $f(T)$ gravity and may offer useful insights for future observational tests of extra dimensions.