Mass hierarchy, mass gap and corrections to Newton’s law on thick branes with Poincaré symmetry

  • Nandinii Barbosa-Cendejas
  • Alfredo Herrera-Aguilar
  • Konstantinos Kanakoglou
  • Ulises Nucamendi
  • Israel Quiros
Research Article


We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with \(m^2\ge 0\), in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza–Klein (KK) excitations and to analytically compute the corrections to Newton’s law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall–Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken–Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar–tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.


Mass hierarchy Mass gap Thick braneworlds Corrections to Newton’s law 



Two of the authors (AHA and IQ) are really grateful to C. Germani, R. Maartens, D. Malagón-Morejón, and S. L. Parameswaran for fruitful and illuminating discussions while this investigation was carried out. AHA and KK also thank B. Figueiredo for useful correspondence and comments. AHA is grateful to the staff of the ICF, UNAM and MCTP, UNACH for hospitality. This research was supported by grants CIC-UMSNH, CONACYT 60060-J, COECYT, Instituto Avanzado de Cosmología (IAC), the MES of Cuba, PAPIIT, UNAM, No. IN103413-3, Teorías de Kaluza-Klein, inflación y perturbaciones gravitacionales and by the research grant 89298 (2013) granted from the Research Committee of the Aristotle University of Thessaloniki. NBC acknowledges a PhD grant from CONACYT and a postdoctoral grant from DGAPA-UNAM. KK is grateful to the Institute of Physics and Mathematics (IFM) of the University of Michoacan (UMSNH) for hospitality and acknowledges support from a postdoctoral scholarship during 2011 from the Research Committee of the Aristotle University of Thessaloniki. NBC, AHA and UN are grateful to SNI for support, while IQ was supported by “Programa PRO-SNI, Universidad de Guadalajara” under Grant No. 146912.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Nandinii Barbosa-Cendejas
    • 1
    • 2
  • Alfredo Herrera-Aguilar
    • 1
    • 3
    • 4
  • Konstantinos Kanakoglou
    • 4
    • 5
  • Ulises Nucamendi
    • 4
  • Israel Quiros
    • 6
  1. 1.Instituto de Ciencias FísicasUniversidad Nacional Autónoma de MéxicoCuernavacaMexico
  2. 2.Facultad de Ingeniería EléctricaUniversidad Michoacana de San Nicolás de HidalgoMoreliaMexico
  3. 3.Mesoamerican Centre for Theoretical PhysicsUniversidad Autónoma de ChiapasTuxtla GutierrezMexico
  4. 4.Instituto de Física y MatemáticasUniversidad Michoacana de San Nicolás de HidalgoMoreliaMexico
  5. 5.School of Mathematics, Faculty of SciencesAristotle University of ThessalonikiThessalonikiGreece
  6. 6.Departamento de Matemáticas, CUCEIUniversidad de GuadalajaraGuadalajaraMexico

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