Scalar perturbations of Eddington-inspired Born-Infeld braneworld

We consider the scalar perturbations of Eddington-inspired Born-Infeld braneworld models in this paper. The dynamical equation for the physical propagating degree of freedom $\xi(x^\mu,y)$ is achieved by using the Arnowitt-Deser-Misner decomposition method: $F_1(y) {\partial_y^2 \xi} + F_2(y){\partial_y \xi } + {\partial^{\mu}\partial_{\mu}}\xi=0$. We conclude that the solution is tachyonic-free and stable under scalar perturbations for $F_1(y)>0$ but unstable for $F_1(y)< 0$. The stability of a known analytic domain wall solution with the warp factor given by $a(y)= \text{sech}^{\frac{3}{{4p}}}(ky)$ is analyzed and it is shown that only the solution for $0<p<\sqrt{8/3}$ is stable.
Comment: 16 pages, 1 figure, accepted by Physical Review D