Constraints on generalized Eddington-inspired Born-Infeld branes

The Palatini $f(|\widehat{\mathrm{\Omega }}|)$ gravity is a generalized theory of the Eddington-inspired Born-Infeld gravity, where ${{\mathrm{\Omega }}^K}_N\equiv {{\delta }^K}_N+b{g}^{KL}{R}_{LN}(\mathrm{\Gamma })$ is an auxiliary tensor constructed with the spacetime metric $g$ and independent connection $\mathrm{\Gamma }$. In this paper, we study $f(|\widehat{\mathrm{\Omega }}|)$ theory with $f(|\widehat{\mathrm{\Omega }}|)=|\widehat{\mathrm{\Omega }}{|}^{\frac{1}{2}+n}$ in the thick brane scenario and give some constraints on the brane model. We finally found an analytic solution of the thick brane generated by a single scalar field. The behavior of the negative energy density denotes the localization of the thick brane at the origin of the extra dimension. In our braneworld, the warp factor is divergent at the boundary of the extra dimension while the brane system is asymptotically anti–de Sitter. It is shown that the tensor perturbation of the brane is stable and the massless graviton is localized on the thick brane. Therefore, the effective Einstein-Hilbert action on the brane can be rebuilt in the low-energy approximation. According to the recent test of the gravitational inverse-square law, we give some constraints on the $f(|\widehat{\mathrm{\Omega }}|)$ brane.

Figure 1

The shapes of the thick brane solution. (a) The warp factor $a(y)$. (b) The scalar field $\varphi (y)$. (c) The scalar potential $V(y)$. (d) The energy density $\rho (y)$. (e) The curvature scalar $R(y)$. The parameters are set to $\kappa =1$, $k=1$, $\lambda =1$, along with $n=5/2$ (blue solid line), $n=9/2$ (red dashed line), and $n=13/2$ (black dotted line).

Figure 2

The shapes of the effective potential, the massless graviton, and the function $z(y)$. (a) The effective potential $U(y)$. (b) The massless graviton ${\psi }_0(y)$ in the $y$ coordinate. (c) The function $z(y)$. (d) The the massless graviton ${\psi }_0(z)$ in the $z$ coordinate. The parameter $n$ is set to $n=5/2$ (blue solid line), $9/2$ (red dashed line), and $13/2$ (black dotted line), and the parameters $\kappa$, $k$, and $\lambda$ are set to unity for convenience.

Figure 3

The relation between the parameters ${\lambda }_i$ and $(n)$. (a) ${\lambda }_1(n)$ defined in Eq. (80). (b) ${\lambda }_2(n)$ defined in Eq. (83). (c) ${\lambda }_3(n)$ defined in Eq. (90). (d) ${\lambda }_4(n)$ defined in Eq. (92). The blue dashed lines denote the value of the parameters with $n$ approaching to $1/2$, while the orange dashed lines localize the extreme points of the parameters.

Figure 4

The constraints on (a) the parameter $k$, (b) the length of the extra dimension $L$, and (c) the mass of the $n^{\prime }$th graviton KK mode $m_{n^{\prime }}$. The areas with color show the allowed regions of $k$, $L$, and $m_{n^{\prime }}$ with respect to different values of $r_c$.