Comptes Rendus
no. 1
Partial differential equations/Mathematical physics
Wave fluctuations near a de Sitter brane in an anti-de Sitter universe
[Propagation des ondes près d'une brane de de Sitter dans un univers anti-de Sitter]

Présenté par : Yvonne Choquet-Bruhat

Alain Bachelot1
1 Université de Bordeaux, Institut de mathématiques, UMR CNRS 5251, 33405 Talence cedex, France
Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 19-25.

Nous étudions l'équation de Klein–Gordon dans le domaine causal passé d'une brane de de Sitter incluse dans un espace anti-de Sitter. Nous résolvons le problème mixte hyperbolique et prouvons que les solutions d'énergie finie s'expriment comme superposition de champs libres dans le demi-espace de de Sitter et nous en étudions les comportements asymptotiques. Nous montrons que le terme dominant des fluctuations gravitationnelles est un graviton sans masse, ce qui traduit la stabilité linéaire de la brane.

We investigate the Klein–Gordon equation in the past causal domain of a de Sitter brane imbedded in an anti-de Sitter bulk. We solve the global mixed hyperbolic problem. We prove that any finite energy solution can be expressed as a Kaluza–Klein tower that is a superposition of free fields in the Steady State Universe, of which we study the asymptotic behaviors. We show that the leading term of a gravitational fluctuation is a massless graviton, i.e. the de Sitter brane is linearly stable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.09.023
Alain Bachelot 1

1 Université de Bordeaux, Institut de mathématiques, UMR CNRS 5251, 33405 Talence cedex, France 
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Alain Bachelot. Wave fluctuations near a de Sitter brane in an anti-de Sitter universe. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 19-25. doi : 10.1016/j.crma.2015.09.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.023/

[1] A. Bachelot Wave propagation and scattering for the RS2 brane cosmology model, J. Hyperbolic Differ. Equ., Volume 6 (2009), pp. 809-861

[2] A. Bachelot The Klein–Gordon equation in the anti-de Sitter cosmology, J. Math. Pures Appl., Volume 96 (2011), pp. 527-554

[3] A. Bachelot New dynamics in the anti-de Sitter universe AdS5, Commun. Math. Phys., Volume 320 (2013), pp. 723-759

[4] A. Bachelot On the Klein–Gordon equation near a de Sitter brane in an anti-de Sitter bulk | arXiv

[5] A. Campos; C.F. Sopuerta Evolution of cosmological models in the brane-world scenario, Phys. Rev. D, Volume 63 (2001)

[6] A. Galstian; K. Yagdjian Fundamental solutions for the Klein–Gordon equation in de Sitter spacetime, Commun. Math. Phys., Volume 285 (2009), pp. 293-344

[7] S. Kobayashi; K. Koyama; J. Soda Thick brane worlds and their stability, Phys. Rev. D, Volume 65 (2001)

[8] D. Langlois; M. Sasaki Massive scalar states localized on a de Sitter brane, Phys. Rev. D, Volume 68 (2003)

[9] M. Minamitsuji; M. Sasaki Linearized gravity on the de Sitter brane in the Einstein Gauss–Bonnet theory, Prog. Theor. Phys., Volume 112 (2004), pp. 451-473

[10] M.K. Parikh; S.N. Solodukhin De Sitter brane gravity: from close-up to panorama, Phys. Lett. B, Volume 503 (2001), pp. 384-393

[11] A. Vasy The wave equation on asymptotically de Sitter-like spaces, Adv. Math., Volume 223 (2010), pp. 49-97

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