Quasinormal modes of scalar perturbations in Rastall thick brane

We investigate quasinormal modes of the graviscalar sector in a five-dimensional thick brane model in Rastall gravity. By considering a specific flat brane solution supported by a canonical scalar field, we derive a master equation and reduce it to a Schr\"odinger-like eigenvalue problem for the Kaluza-Klein modes. Using the Bernstein spectral method and direct integration in the frequency domain, complemented by numerical time-domain evolutions, we compute the complex quasinormal frequencies for the scalar perturbations. Our results reveal a strong dependence of the QNM spectrum on $\lambda$: the imaginary parts of the frequencies, governing the decay rate, decrease monotonically with increasing $\lambda$, indicating longer-lived modes. The real parts exhibit a more complex, non-monotonic behavior. Furthermore, we analyze the late-time behavior of the perturbations, showing that the asymptotic tail follows a power law whose exponent is determined by the Rastall parameter, in agreement with theoretical predictions for the asymptotic form of the potential. These findings provide a comprehensive dynamical characterization of the scalar sector of Rastall thick branes, offering potential observational signatures for probing modified gravity in extra-dimensional scenarios.