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arXiv · 2609.37346

Relic of the Kink Shape Mode in a Topological Thick Brane - some implications

Gahan Chattopadhyay·Soumitra Sengupta
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Abstract

The kink soliton provides a simple construction of a topological thick 3-brane sourced by a minimally coupled canonical scalar field in five-dimensional general relativity. Although the flat-space kink is a solution of $φ^4$ theory, the gravitating configuration requires $M_*$-suppressed $φ^6$ corrections to support a stable warped geometry. Unlike its flat-space counterpart, the scalar perturbation spectrum contains no normalizable bound state. We nevertheless identify a single quasi-bound, or resonant, mode. Using a time-independent relative-probability analysis, direct time evolution, and a four-turning-point WKB calculation, we establish a direct connection between this resonance and the massive bound shape mode of the flat-space $φ^4$ kink. We also show that, within an EFT-consistent parameter window, the resonance can transfer energy from bulk geometric fluctuations to localized matter, thereby allowing the possibility of high-scale reheating in the early universe.

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Gahan Chattopadhyay, Soumitra Sengupta. 2026-09-29. Relic of the Kink Shape Mode in a Topological Thick Brane - some implications. https://arxiv.org/abs/2609.37346

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