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Cosmological constraints for a two branes system in a vacuum bulk

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Abstract

We study a two 3-branes system embedded in a 5-dimensional spacetime with the fifth dimension compactified on a \(S^{1}/Z_{2}\) orbifold. Assuming isotropic and homogeneous branes, we show that the dynamics of the visible brane affects the hidden brane through gravitational interaction. This influence is described by equations that relate the matter contents on each brane, and arise from the Israel’s junction conditions. We analyse the case in which both branes are composed of a single matter field with a vacuum bulk, and explore the different possibilities allowed for the cosmologies of the branes.

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Notes

  1. Notice that we are using units with \(c=\hbar =1\), and that indices are \(\mu ,\nu = 0,1,2,3, i,j=1,2,3\), and \(A,B = 0,1,2,3,4\).

  2. Equation (11) can be analytically solved if \(b=a^m\) and \(m=0,-1,1\). The case \(m=0\) can actually be found in [17], whereas the other two cases can be solved in terms of elliptic functions.

  3. The following inequality is valid for \(m < 3(1+ \omega )\) otherwise it is reversed except for \(m=3(1+ \omega )\) where the expression inside the absolute value is a constant.

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Acknowledgments

We thank M. A. García-Aspeitia for useful comments. LAU-L thanks the Royal Observatory, Edinburgh, where part of this work was done during a sabbatical stay, for its kind hospitality. We acknowledge partial support by SNI-México, CONACyT research Grants J1-60621-I, 103478, COFAA-IPN and SIP-IPN Grant 20131541 and 20144150. This work was partially supported by PIFI, PROMEP, DAIP-UG, CONACyT México under Grants 167335 and 179881, the Fundación Marcos Moshinsky, and the Instituto Avanzado de Cosmología (IAC) collaboration.

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  1. L. Arturo Ureña-López

    Present address: Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ, UK

Authors and Affiliations

  1. Departamento de Física, Universidad de Guanajuato, DCI, Campus León, 37150, León, GTO, México

    Juan Luis Pérez & L. Arturo Ureña-López

  2. Departamento de Física, Escuela Superior de Física y Matemáticas del IPN, Instituto Politécnico Nacional, Unidad Adolfo López Mateos, Edificio 9, 07738, México, D.F., México

    Rubén Cordero

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  1. Juan Luis Pérez
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Correspondence to Rubén Cordero.

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Pérez, J.L., Ureña-López, L.A. & Cordero, R. Cosmological constraints for a two branes system in a vacuum bulk. Gen Relativ Gravit 47, 2 (2015). https://doi.org/10.1007/s10714-014-1847-3

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