Tachyonic perturbations in AdS$_5$ orbifolds

TL;DR

This paper investigates the presence of tachyonic perturbations in the Randall-Sundrum II braneworld, showing potential instabilities linked to initial anisotropic stresses and orbifold singularities, with implications for cosmology.

Contribution

It demonstrates the existence of normalizable tachyonic modes in the RSII model and explores their stability and origin, especially in cosmological scenarios.

Findings

Tachyonic modes exist in RSII perturbations.

No instability occurs in a specific RSII example.

Orbifold singularity may cause tachyonic modes.

Abstract

We show that scalar as well as vector and tensor metric perturbations in the Randall-Sundrum II braneworld allow normalizable tachyonic modes, i.e., possible instabilities. These instabilities require nonvanishing initial anisotropic stresses on the brane. We show with a specific example that within the Randall-Sundrum II model, even though the tachyonic modes are excited, no instability develops. We argue, however, that in the cosmological context instabilities might in principle be present. We conjecture that the tachyonic modes are due to the singularity of the orbifold construction. We illustrate this with a simple but explicit toy model.