Wave fluctuations near a de Sitter brane in an anti-de Sitter universe

Alain Bachelot

doi:10.1016/j.crma.2015.09.023

Partial differential equations/Mathematical physics

Wave fluctuations near a de Sitter brane in an anti-de Sitter universe

Presented by: Yvonne Choquet-Bruhat

Alain Bachelot ¹

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.

Abstract
Résumé

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.

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.

Received: 2014-03-05
Accepted: 2015-09-28
Published online: 2015-11-02

DOI: 10.1016/j.crma.2015.09.023

Author's affiliations:

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/

References
Cited by

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