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On localization of universal scalar fields in a tachyonic de Sitter thick braneworld

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Abstract

Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used, for example, to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld possesses a 4D de Sitter induced metric and is asymptotically flat despite the presence of a negative bulk cosmological constant, a novel and interesting peculiarity that contrasts with previously known models. It turns out that universal scalar fields can be localized in this expanding braneworld if their bulk mass obeys an upper bound, otherwise the scalar fields delocalize: The dynamics of the scalar field is governed by a Schrödinger equation with an analog quantum mechanical potential of modified Pöschl–Teller type. This potential depends on the bulk curvature of the braneworld system as well as on the value of the bulk scalar field mass. For masses satisfying a certain upper bound, the potential displays a negative minimum and possesses a single massless bound state separated from the Kaluza–Klein (KK) massive modes by a mass gap defined by the Hubble (expansion scale) parameter of the 3-brane. As the bulk scalar field mass increases, the minimum of the quantum mechanical potential approaches a null value and, when the bulk mass reaches certain upper bound, it becomes positive (eventually transforming into a potential barrier), leading to delocalization of the bulk scalar field from the brane. We present analytical expressions for the general solution of the Schrödinger equation. Thus, the KK massive modes are given in terms of general Heun functions as well as the expression for the massless zero mode, giving rise to a new application of these special functions.

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Acknowledgments

AHA and RRML acknowledge useful and illuminating discussions with Dagoberto Malagón Morejón. AHA is grateful to ICF, UNAM and UAM-I for hospitality, as well as to “Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica” (PAPIIT) UNAM, IN103413-3, Teorías de Kaluza–Klein, inflación y perturbaciones gravitacionales for financial support. ADF gratefully acknowledge support from the PROMEP program Becas Posdoctorales en Cuerpos Académicos consolidados y en consolidación under the Grant No. 12312096. RRML acknowledges a postdoctoral Grant from CONACyT at ICF-UNAM. All authors thank SNI.

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Authors and Affiliations

  1. Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, CP 09340, Mexico, D.F., Mexico

    Alfonso Díaz-Furlong, Alfredo Herrera-Aguilar, Román Linares & Hugo A. Morales-Técotl

  2. Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, CP 58040, Morelia, Michoacán, Mexico

    Alfredo Herrera-Aguilar

  3. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apdo. Postal 48-3, 62251, Cuernavaca, Morelos, Mexico

    Refugio Rigel Mora-Luna

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  1. Alfonso Díaz-Furlong
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  2. Alfredo Herrera-Aguilar
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  3. Román Linares
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  4. Refugio Rigel Mora-Luna
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  5. Hugo A. Morales-Técotl
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Correspondence to Alfredo Herrera-Aguilar.

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Díaz-Furlong, A., Herrera-Aguilar, A., Linares, R. et al. On localization of universal scalar fields in a tachyonic de Sitter thick braneworld. Gen Relativ Gravit 46, 1815 (2014). https://doi.org/10.1007/s10714-014-1815-y

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