Cosmic Strings in a Braneworld Theory with Metastable Gravitons

TL;DR

The paper studies cosmic strings in a braneworld theory with metastable gravitons, showing that nonperturbative effects on the brane restore Einstein gravity near the string despite perturbative VDVZ-like behavior. By deriving and matching linearized and nonlinear solutions in different brane regimes, the author demonstrates a Vainshtein-type mechanism: near the string the brane extrinsic curvature suppresses the scalar mode, while far from the string a scale-dependent Newtonian potential emerges. The results indicate there is no discontinuity in the full nonlinear theory, and they reveal a region of scale-dependent metric structure that could affect gravitational lensing searches for cosmic strings. This work supports the view that metastable-brane gravity can reproduce Einstein gravity in appropriate limits while yielding distinctive, testable predictions at intermediate scales.

Abstract

If the graviton possesses an arbitrarily small (but nonvanishing) mass, perturbation theory implies that cosmic strings have a nonzero Newtonian potential. Nevertheless in Einstein gravity, where the graviton is strictly massless, the Newtonian potential of a cosmic string vanishes. This discrepancy is an example of the van Dam--Veltman--Zakharov (VDVZ) discontinuity. We present a solution for the metric around a cosmic string in a braneworld theory with a graviton metastable on the brane. This theory possesses those features that yield a VDVZ discontinuity in massive gravity, but nevertheless is generally covariant and classically self-consistent. Although the cosmic string in this theory supports a nontrivial Newtonian potential far from the source, one can recover the Einstein solution in a region near the cosmic string. That latter region grows as the graviton's effective linewidth vanishes (analogous to a vanishing graviton mass), suggesting the lack of a VDVZ discontinuity in this theory. Moreover, the presence of scale dependent structure in the metric may have consequences for the search for cosmic strings through gravitational lensing techniques.

Figures (2)

• Figure 1: A schematic representation of a spatial slice through a cosmic string located at $A$. The coordinate $x$ along the cosmic string is suppressed. The coordinate $r$ represents the 3-dimensional distance from the cosmic string $A$, while the coordinate $z$ denotes the polar angle from the vertical axis. In the no-gravity limit, the braneworld is the horizontal plane, $z = {\pi\over 2}$. The coordinate $\phi$ is the azimuthal coordinate. Note that everywhere except at the cosmic string, the unit vector in the direction of the $z$-coordinate extends perpendicularly from the brane into the bulk.
• Figure 2: A spatial slice through the cosmic string located at $A$. As in Fig. \ref{['fig:flat']} the coordinate $x$ along the cosmic string is suppressed. The solid angle wedge exterior to the cone is removed from the space, and the upper and lower branches of the cone are identified. This conical surface is the braneworld ($z={\pi\alpha\over 2}$ or $\sin z = \beta$). The bulk space now exhibits a deficit polar angle (cf. Fig. \ref{['fig:flat']}). Note that this deficit in polar angle translates into a conical deficit in the braneworld space.