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Quantum modified Regge–Teitelboim cosmology

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An Erratum to this article was published on 19 July 2014

Abstract

The canonical quantization of the modified geodetic brane cosmology which is implemented from the Regge–Teitelboim model and the trace of the extrinsic curvature of the brane trajectory, \(K\), is developed. As a second-order derivative model, on the grounds of the Ostrogradski Hamiltonian method and the Dirac’s scheme for constrained systems, we find suitable first- and second-class constraints which allow for a proper quantization. We also find that the first-class constraints obey a sort of truncated Virasoro algebra. The effective quantum potential emerging in our approach is exhaustively studied where it shows that an embryonic epoch is still present. The quantum nucleation is sketched where we observe that it is driven by an effective cosmological constant.

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Notes

  1. This fact is supported by using an existing completeness relation in the geometry of deformations for branes, namely \(\eta ^{\mu \nu } = n^\mu n^\nu - \eta ^\mu \eta ^\nu + h^{AB} \epsilon ^\mu {}_A \epsilon ^\nu {}_B\). See Ref. [31].

  2. This function is given by the relation

    $$\begin{aligned} G (a,N,v,\varPi _v) := \left[ \frac{2}{a^3} \left( v - a^2 \cosh \varPi _v - \bar{\beta } a^3 \right) - \bar{\varLambda } \left( \sqrt{\gamma } + \frac{a}{2\sqrt{\gamma }} \frac{\partial \gamma }{\partial a} \right) \right] N \sinh \varPi _v. \end{aligned}$$

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Acknowledgments

The authors are grateful to Alexander Vilenkin for helpful discussions. AM acknowledges support from PROMEP UASLP-PTC-402. ER acknowledges partial support from Grant PROMEP, CA-UV: Algebra, Geometría y Gravitación. M.C. was supported by PUCV through Proyecto DI Postdoctorado 2014. Also, E.R. and M.C. acknowledge partial support from the Grant CONACyT CB-2012-01-177519. This work was partially supported by SNI (México). RC also acknowledges support from EDI, COFAA-IPN, SIP-20131541 and SIP-20144150.

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Authors and Affiliations

  1. Departamento de Física, Escuela Superior de Física y Matemáticas del I.P.N., Unidad Adolfo López Mateos, Edificio 9, 07738 , México, DF, México

    Rubén Cordero

  2. Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4950, Valparaiso, Chile

    Miguel Cruz

  3. Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Av. Salvador Nava S/N, Zona Universitaria, CP 78290, San Luis Potosí, SLP, México

    Alberto Molgado

  4. Dual CP Institute of High Energy Physics, México, México

    Alberto Molgado

  5. Departamento de Física, Facultad de Física e Inteligencia Artificial, Universidad Veracruzana, 91000 , Xalapa, VER, México

    Efraín Rojas

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  1. Rubén Cordero
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  2. Miguel Cruz
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  3. Alberto Molgado
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  4. Efraín Rojas
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Correspondence to Efraín Rojas.

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Cordero, R., Cruz, M., Molgado, A. et al. Quantum modified Regge–Teitelboim cosmology. Gen Relativ Gravit 46, 1761 (2014). https://doi.org/10.1007/s10714-014-1761-8

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