Complex scalar field thick branes: stability of linear perturbation and evolution of scalar Kaluza-Klein modes coupled with gravity
Abstract
We investigate the stability and localization properties of Minkowski, de Sitter (dS), and anti-de Sitter (AdS) thick branes generated by a complex scalar field Φ. The scalar self-interaction potential contains a temperature parameter a. As a approaches its critical value, the imaginary part of Φ becomes double-kinked and the energy density splits into two peaks, indicating the formation of two sub-branes. The analysis of linear scalar, vector, and tensor perturbations shows no signs of instability in the scalar and vector sectors, while the factorization of the tensor perturbation equation excludes tachyonic tensor modes. The graviton zero mode is localized on the Minkowski and dS branes but is not normalizable on the AdS brane. We further study a real test scalar field Ψ with a coupling function F(R) between its kinetic term and the spacetime curvature. The scalar zero mode can always be localized on the Minkowski and dS branes, with a continuous gapless spectrum of scalar Kaluza--Klein (KK) modes. Massive scalar resonances emerge near the critical value of a for suitable values of β. Increasing β produces more resonances and prolongs the lifetimes of the lower resonances, while their time evolution exhibits the characteristic decay of metastable modes. For the AdS brane, the scalar zero mode is also localized, whereas the divergent effective potential at the boundaries traps the massive scalar KK modes as bound states, yielding a discrete mass spectrum.
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BibTeX
@misc{dong2026complex,
title = {{Complex scalar field thick branes: stability of linear perturbation and evolution of scalar Kaluza-Klein modes coupled with gravity}},
author = {Wang-Long Dong and Heng Guo and Qun Wei and Yong-Tao Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21421},
eprint = {2609.21421},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21421},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Complex scalar field thick branes: stability of linear perturbation and evolution of scalar Kaluza-Klein modes coupled with gravity
AU - Wang-Long Dong
AU - Heng Guo
AU - Qun Wei
AU - Yong-Tao Lu
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21421
UR - https://arxiv.org/abs/2609.21421
AB - We investigate the stability and localization properties of Minkowski, de Sitter (dS), and anti-de Sitter (AdS) thick branes generated by a complex scalar field Φ. The scalar self-interaction potential contains a temperature parameter a. As a approaches its critical value, the imaginary part of Φ becomes double-kinked and the energy density splits into two peaks, indicating the formation of two sub-branes. The analysis of linear scalar, vector, and tensor perturbations shows no signs of instability in the scalar and vector sectors, while the factorization of the tensor perturbation equation excludes tachyonic tensor modes. The graviton zero mode is localized on the Minkowski and dS branes but is not normalizable on the AdS brane. We further study a real test scalar field Ψ with a coupling function F(R) between its kinetic term and the spacetime curvature. The scalar zero mode can always be localized on the Minkowski and dS branes, with a continuous gapless spectrum of scalar Kaluza--Klein (KK) modes. Massive scalar resonances emerge near the critical value of a for suitable values of β. Increasing β produces more resonances and prolongs the lifetimes of the lower resonances, while their time evolution exhibits the characteristic decay of metastable modes. For the AdS brane, the scalar zero mode is also localized, whereas the divergent effective potential at the boundaries traps the massive scalar KK modes as bound states, yielding a discrete mass spectrum.
ER -