[Propagation des ondes près d'une brane de de Sitter dans un univers anti-de Sitter]
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.
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@article{CRMATH_2016__354_1_19_0,
author = {Bachelot, Alain},
title = {Wave fluctuations near a de {Sitter} brane in an anti-de {Sitter} universe},
journal = {Comptes Rendus. Math\'ematique},
pages = {19--25},
publisher = {Elsevier},
volume = {354},
number = {1},
year = {2016},
doi = {10.1016/j.crma.2015.09.023},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2015.09.023/}
}
TY - JOUR AU - Bachelot, Alain TI - Wave fluctuations near a de Sitter brane in an anti-de Sitter universe JO - Comptes Rendus. Mathématique PY - 2016 SP - 19 EP - 25 VL - 354 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2015.09.023/ DO - 10.1016/j.crma.2015.09.023 LA - en ID - CRMATH_2016__354_1_19_0 ER -
%0 Journal Article %A Bachelot, Alain %T Wave fluctuations near a de Sitter brane in an anti-de Sitter universe %J Comptes Rendus. Mathématique %D 2016 %P 19-25 %V 354 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2015.09.023/ %R 10.1016/j.crma.2015.09.023 %G en %F CRMATH_2016__354_1_19_0
Bachelot, Alain. Wave fluctuations near a de Sitter brane in an anti-de Sitter universe. Comptes Rendus. Mathématique, Tome 354 (2016) no. 1, pp. 19-25. doi : 10.1016/j.crma.2015.09.023. http://archive.numdam.org/articles/10.1016/j.crma.2015.09.023/
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