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arXiv · 2605.18403

Tachyonic (In)stability in Randall-Sundrum Braneworld Scenarios

Abhirup Karmakar·Soumitra SenGupta
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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 brane 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 with the on-brane dS$_4$ and AdS$_4$ geometries.

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Abhirup Karmakar, Soumitra SenGupta. 2026-05-18. Tachyonic (In)stability in Randall-Sundrum Braneworld Scenarios. https://arxiv.org/abs/2605.18403

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