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Induced Matter Theory of gravity from a Weitzenböck 5D vacuum and pre-big bang collapse of the universe

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Abstract

We extend the Induced Matter Theory of gravity (IMT) to 5D curved spacetimes by using the Weitzenböck representation of connections on a 5D curved spacetime. In this representation the 5D curvature tensor becomes null, so that we can make a static foliation on the extra non-compact coordinate to induce in the Weitzenböck representation the Einstein equations. Once we have done it, we can rewrite the effective 4D Einstein equations in the Levi-Civita representation. This generalization of IMT opens a huge window of possible applications for this theory. A pre-big bang collapsing scenario is explored as an example.

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Notes

  1. In our conventions indices “a,b,c,…,h” run from 1 to 5, “A,B,C,…,H” run from 1 to 5, Greek indices α,β,γ run from 1 to 4 and indices “i,j,k,…” run from 2 to 4.

  2. Notice that for fermionic fields (for instance with spin 1/2), the Cartan equation (22) should be

    $$ \overbrace{{S}_{\beta\gamma}}^{\mathrm{4D}} - \frac{1}{2} \sigma_{\beta\gamma} S =-8 \pi G \,\underbrace{\overbrace {{T}_{\beta\gamma}}^{\mathrm{4D}}}_{(\mathrm{ant})}, $$

    where S=σ μν S μν , \(\sigma^{\mu\nu}={1\over2} [\gamma^{\mu}, \gamma^{\nu} ]\) and γ μ are the Dirac matrices. However, this issue is beyond the scope of this work.

  3. In the cases where \(M_{\mathrm{eff}}^{2} >0\) and the universe expands with a nearly constant energy density given by ρ≃〈V(φ)〉 and a pressure P≃−〈V(φ)〉, the potential (55) is a good candidate to describe inflation.

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Acknowledgements

The authors acknowledge P.S. Wesson for his interesting comments. Furthermore, we acknowledge UNMdP and CONICET Argentina for financial support.

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Authors and Affiliations

  1. Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata, Argentina

    Jesús Martín Romero & Mauricio Bellini

  2. Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata, Argentina

    Mauricio Bellini

Authors
  1. Jesús Martín Romero
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  2. Mauricio Bellini
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Correspondence to Mauricio Bellini.

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Romero, J.M., Bellini, M. Induced Matter Theory of gravity from a Weitzenböck 5D vacuum and pre-big bang collapse of the universe. Eur. Phys. J. C 73, 2317 (2013). https://doi.org/10.1140/epjc/s10052-013-2317-x

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  • DOI: https://doi.org/10.1140/epjc/s10052-013-2317-x

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