Cosmic Strings in a Braneworld Theory with Metastable Gravitons

TL;DR

This paper explores the gravitational field of cosmic strings in a braneworld model with metastable gravitons, showing how it can mimic Einstein gravity near the string while exhibiting a nonzero potential far away, potentially affecting gravitational lensing observations.

Contribution

It provides a self-consistent solution for cosmic strings in a braneworld with metastable gravitons, demonstrating the absence of the VDVZ discontinuity and implications for gravitational lensing.

Findings

Cosmic strings exhibit a nonzero Newtonian potential far from the source.

Near the string, the solution recovers Einstein gravity, indicating no VDVZ discontinuity.

Scale-dependent metric features could influence gravitational lensing searches.

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.