Graviscalar quasinormal modes and asymptotic tails of a thick brane

In this work, we investigate the quasinormal modes (QNMs) and the late time oscillatory tails of graviscalar perturbations in a thick brane. By considering the scalar perturbations of the thick brane metric, we obtain the main equations of graviscalar Kaluza-Klein modes. Using these equations, the frequencies of the graviscalar QNMs of the thick brane are obtained by the Wentzel-Kramers-Brillouin, asymptotic iteration, and numerical evolution methods. The results show that the scalar fluctuation of the thick brane has a series of discrete QNMs. In the four-dimensional spacetime, these modes manifest as decaying massive scalar particles. We also study in detail the late time tails of the scalar fluctuation. We find that the brane has slowly decaying oscillatory tails that may be new sources of the gravitational wave backgrounds. These novel phenomena may have potential phenomenological significance, and signals from these extra dimensions may potentially be found in current or future gravitational wave detectors.