Tachyonic (In)stability in Randall-Sundrum Braneworld Scenarios

TL;DR

This paper investigates tachyonic instabilities and spontaneous scalarization in Randall-Sundrum braneworld models, analyzing radion stability under various conditions and extending the formalism to $f(R)$ gravity theories relevant to cosmology.

Contribution

It provides a detailed analysis of radion tachyonic stability in different RS scenarios and extends the formalism to $f(R)$ theories, offering insights into brane-world cosmology.

Findings

Radion stability depends on on-brane matter and potential configurations.

On-brane matter with $T>0$ destabilizes the radion, affecting the hierarchy problem.

Conditions for radion (in)stability are explicitly derived for various models.

Abstract

Low-energy effective theories provide a natural description of four-dimensional physics in higher-dimensional geometries, where the imprint of the bulk geometry appears as parameters of the lower-dimensional theory. Inspired by the Damour-Esposito-Far\'ese (DEF) model of spontaneous scalarization in first generation Scalar-Tensor theories of gravity, we investigate the possibility of tachyonic instability and spontaneous scalarization in braneworld scenarios. We consider the two-brane Randall-Sundrum model where the low-energy effective theory on either brane is of scalar-tensor nature with the extra-dimensional radion playing the role of the scalar. We have determined the possibilities for tachyonic (in)stability of the radion field on either branes in three scenarios: the Randall-Sundrum (RS) model with fine-tuning conditions in which the potential of the radion field vanishes identically, the RS model without fine-tunings where the radion potential arises purely from the gravity sector, and the RS model with a bulk stabilizing field that generates a radion potential with a minimum. With the bulk stabilizing field, we have found that on-brane matter with $T>0$ changes the VEV of the radion, destroying the resolution of the gauge hierarchy problem, whereas on-brane matter with $T<0$ does not alter the stability and VEV of the radion. We further determined the exact condition of tachyonic (in)stability of radion field on Planck brane with the FLRW background geometry on the brane. Finally, we have extended the same formalism to study the tachyonic (in)stability conditions of $f(R)$ theories of gravity with the motivation that the 4D effective theory on RS branes can be casted into a $f(R)$ theory on the branes at the inflationary epoch of cosmology.