Domain Walls As Probes Of Gravity

TL;DR

The paper argues that domain walls are sensitive probes of infrared gravity, using the DGP model to show that low-tension walls are stealth on the brane due to extrinsic-curvature screening, with a characteristic nonlinear scale $r_* \sim (r_g r_c^2)^{1/3}$ (and for walls, $r_*^{(dw)} \sim d$). It derives exact solutions for walls on both the Conventional Branch and the Self-Accelerated Branch, revealing complete 4D-tension screening for sub-critical walls on CB, anti-screening on SAB, and a distinct behavior for super-critical walls where the 5D tension is screened and the transverse space tightens to the wall thickness. The results are extended to a broader class of IR-modified gravity theories, where nonlinearities determine a domain-wall scale $r_*$ and dictate whether walls reveal deviations from GR. Overall, domain walls provide a concrete, nonperturbative handle to distinguish modified gravity from GR at short scales, with implications for testing the nature of gravity in the infrared.

Abstract

We show that domain walls are probes that enable one to distinguish large-distance modified gravity from general relativity (GR) at short distances. For example, low-tension domain walls are stealth in modified gravity, while they do produce global gravitational effects in GR. We demonstrate this by finding exact solutions for various domain walls in the DGP model. A wall with tension lower than the fundamental Planck scale does not inflate and has no gravitational effects on a 4D observer, since its 4D tension is completely screened by gravity itself. We argue that this feature remains valid in a generic class of models of infrared modified gravity. As a byproduct, we obtain exact solutions for super-massive codimension-2 branes.

Figures (4)

• Figure 1: The brane trajectory in the $R-Z$ plane, for a generic DW in an inflating brane $(H\neq0)$. The two figures represent a constant time snapshot, and one of the directions along the DW (represented by the thick dot) is obtained in the upper diagram by rotating it around the $Z$ (vertical) axis. The space is cut by the two constant $Z$ sections where the brane is at an angle $\alpha=H\xi_0$. The space in between is then removed, and the two slices joined together. Then, another identical copy of the resulting 'pancake' is glued along the brane, as indicated in the lower diagram. For the conventional branch (CB), the bulk is the interior, while for the self-accelerated branch (SAB), it is the exterior. For the CB, this space has a deficit angle $\delta=4\beta$, with $\beta=\pi/2-\alpha$. For the SAB, we have an excess angle, that is $\delta=-4\beta$.
• Figure 2: Conical space corresponding to the flat DW case in a flat brane. The deficit angle is $\delta=4\beta$, which is always less than $2\pi$. This figure refers to the Conventional Branch, and with zero brane tension.
• Figure 3: The radius of the DW $R_0$ for the conventional branch (CB), in the $Z_2$ symmetric case, for $Hr_c=0.2,0.01$ and $0$, and the deficit angle (for $Hr_c=0.01$) as a function of the tension $\sigma$. We see how the DW tension is screened by the $K_{\mu\nu}$ term (contributing effectively negative tension), so that the radius of the DW is larger than in 4D GR (dashed line). There is a qualitative change of behavior for tensions below or above the critical value $2\pi M_*^3$ (vertical lines). In the limit $H=0$, tensions smaller than or equal to $2\pi M_*^3$ induce a flat DW. Only for $\sigma>2\pi M_*^3$, the DW worldsheet is inflating, and $R_0$ approaches the 4D value ($r_{dw}$) for $\sigma\gg M_*^3$.
• Figure 4: The deficit angle and the radius $R_0$ of the DW for the Self-Accelerated Branch. The radius $R_0$ approaches its 4D value (dashed line) for large $\sigma$. The fact that $R_0$ is smaller than the GR result is a consequence of the anti-screening produced by the extrinsic curvature term. In the third plot, we see the anti-screened the 4D tension, which amounts to a factor $2$ for small $\sigma$. For large tension, $\sigma^{(4D)}$ approaches the GR result.