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 $a(y)={\mathrm{sech}}^{\frac{3}{4p}}(ky)$ is analyzed and it is shown that only the solution for $0<p<\sqrt{8/3}$ is stable.

Figure 1

The potential $V(z)$ with the parameters $p=\sqrt{2}$, $b=1$ (dotted line), $p=1$, $b=1$ (thick line), and $p=1$, $b=5$ (dashed line).