Screening bulk curvature in the presence of large brane tension

TL;DR

The paper investigates screening of large brane tension within a 5D covariant proxy model for cascading gravity, featuring a brane-bending scalar π with cubic self-interactions. A flat-brane solution in a Minkowski bulk exists for arbitrary tension, enabled by a screening mechanism that reduces the effective bulk curvature, with m6 and M5 setting the relevant scales. However, the perturbative stability analysis reveals ghosts for positive tension and stabilizes only for sufficiently small negative tension, highlighting stringent stability constraints. The work underscores the potential of higher-codimension generalizations for degravitating vacuum energy, while pointing to higher-order galileon terms as a promising route to widen the stable parameter space and maintain viable 4D gravity on the brane.

Abstract

We study a flat brane solution in an effective 5D action for cascading gravity and propose a mechanism to screen extrinsic curvature in the presence of a large tension on the brane. The screening mechanism leaves the bulk Riemann-flat, thus making it simpler to generalize large extra dimension dark energy models to higher codimensions. By studying an action with cubic interactions for the brane-bending scalar mode, we find that the perturbed action suffers from ghostlike instabilities for positive tension, whereas it can be made ghost-free for sufficiently small negative tension.

Figures (2)

• Figure 1: In the left panel, we plot the quantity $\frac{Z^{2}}{2\bar{\Omega}} + \frac{Z\bar{\Omega}_{,\pi}}{\bar{\Omega}} - \frac{9\bar{\pi}"}{8m_{6}^{2}}$ which appears in the ghost-free condition (\ref{['noghostbulk']}) for $\Omega = 1 + 3\pi/2$ and $\Lambda = M_{6}^{4}$. The three curves correspond to the three roots of the cubic equation (\ref{['jcfirstint']}) in $\bar{\pi}'/m_{6}$. The ghost-free condition requires $\frac{Z^{2}}{2\bar{\Omega}} + \frac{Z\bar{\Omega}_{,\pi}}{\bar{\Omega}} - \frac{9\bar{\pi}"}{8m_{6}^{2}} < 0$, hence only the black (solid) curve is free of ghost instabilities. In the right panel, we plot $\bar{\Omega}(y)$ for the ghost-free case. Since $\bar{\Omega}$ vanishes at finite $y$, corresponding to strong coupling, this solution is unphysical. We have found similar results for all positive values of $\Lambda$ and functional forms of $\Omega$ that we have tried.
• Figure 2: Same as Fig. \ref{['fig1']}, except that $\Omega = 1 + 3\pi/2$ and $\Lambda = -M_{6}^{4}$. From the right panel, we see that $\bar{\Omega}(y)$ corresponding to the ghost-free branch is everywhere positive, hence this solution is physically viable.